Materials selection in mechanical design (3rd edition): Part 1

Figure 2.6 The central problem of materials selection in mechanical design: the interaction between function, material, shape and process.. 2.5 Function, material, shape, and process 19.[r]

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Materials Selection in Mechanical Design

Third Edition

Michael F Ashby

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Butterworth-Heinemann

Linacre House, Jordan Hill, Oxford OX2 8DP 30 Corporate Drive, Burlington, MA 01803 First published by Pergamon Press 1992 Second edition 1999

Third edition 2005

Copyright#1992, 1999, 2005 Michael F Ashby All rights reserved The right of Michael F Ashby to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988

No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1T 4LP Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publisher

Permissions may be sought directly from Elsevier’s Science and Technology Rights Department in Oxford, UK: phone: (ỵ44) (0) 1865 843830, fax: (ỵ44) 1865 853333, e-mail: permissions@elsevier.co.uk You may also complete your request on-line via the Elsevier homepage (http://www.elsevier.com), by selecting ‘Customer Support’ and then ‘Obtaining Permissions’

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data

A catalog record for this book is available from the Library of Congress ISBN 7506 6168

For information on all Elsevier Butterworth-Heinemann publications visit our website at http://books.elsevier.com Typeset by Newgen Imaging Systems (P) Ltd, Chennai, India Printed and bound in Italy

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Materials, of themselves, affect us little; it is the way we use them which influences our lives Epictetus, AD 50–100,DiscoursesBook 2, Chapter

New materials advanced engineering design in Epictetus’ time Today, with more materials than ever before, the opportunities for innovation are immense But advance is possible only if a pro-cedure exists for making a rational choice This book develops a systematic propro-cedure for selecting materials and processes, leading to the subset which best matches the requirements of a design It is unique in the way the information it contains has been structured The structure gives rapid access to data and allows the user great freedom in exploring the potential of choice The method is available as software,1giving greater flexibility

The approach emphasizes design with materials rather than materials ‘‘science’’, although the underlying science is used, whenever possible, to help with the structuring of criteria for selection The first eight chapters require little prior knowledge: a first-year grasp of materials and mechanics is enough The chapters dealing with shape and multi-objective selection are a little more advanced but can be omitted on a first reading As far as possible the book integrates materials selection with other aspects of design; the relationship with the stages of design and optimization and with the mechanics of materials, are developed throughout At the teaching level, the book is intended as the text for 3rd and 4th year engineering courses on Materials for Design: a 6–10 lecture unit can be based on Chapters 16; a full 20ỵlecture course, with associated project work with the associated software, uses the entire book

Beyond this, the book is intended as a reference text of lasting value The method, the charts and tables of performance indices have application in real problems of materials and process selection; and the catalogue of ‘‘useful solutions’’ is particularly helpful in modelling — an essential ingre-dient of optimal design The reader can use the book (and the software) at increasing levels of sophistication as his or her experience grows, starting with the material indices developed in the case studies of the text, and graduating to the modelling of new design problems, leading to new material indices and penalty functions, and new — and perhaps novel — choices of material This continuing education aspect is helped by a list of Further reading at the end of most chapters, and by a set of exercises in Appendix E covering all aspects of the text Useful reference material is assembled in appendices at the end of the book

Like any other book, the contents of this one are protected by copyright Generally, it is an infringement to copy and distribute materials from a copyrighted source But the best way to use the charts that are a central feature of the book is to have a clean copy on which you can draw, try out alternative selection criteria, write comments, and so forth; and presenting the conclusion of a selection exercise is often most easily done in the same way Although the book itself is copyrighted, the reader is authorized to make unlimited copies of the charts, and to reproduce these, with proper reference to their source, as he or she wishes

M.F Ashby Cambridge, July 2004 TheCES materials and process selection platform, available from Granta Design Ltd, Rustat House, 62 Clifton Road, Cambridge CB1

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Acknowledgements

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Since publication of the Second Edition, changes have occurred in the fields of materials and mechanical design, as well as in the way that these and related subjects are taught within a variety of curricula and courses This new edition has been comprehensively revised and reorganized to address these Enhancements have been made to presentation, including a new layout and two-colour design, and to the features and supplements that accompany the text The key changes are outlined below

Key changes

New and fully revised chapters:

Processes and process selection (Chapter 7)

Process selection case studies (Chapter 8)

Selection of material and shape (Chapter 11)

Selection of material and shape: case studies (Chapter 12)

Designing hybrid materials (Chapter 13)

Hybrid case studies (Chapter 14)

Information and knowledge sources for design (Chapter 15)

Materials and the environment (Chapter 16)

Materials and industrial design (Chapter 17)

Comprehensive appendices listing useful formulae; data for material properties; material indices; and information sources for materials and processes

Supplements to the Third Edition

Material selection charts

Full color versions of the material selection charts presented in the book are available from the following website Although the charts remain copyright of the author, users of this book are authorized to download, print and make unlimited copies of these charts, and to reproduce these for teaching and learning purposes only, but not for publication, with proper reference to their owner-ship and source To access the charts and other teaching resources, visit www.grantadesign.com/ ashbycharts.htm

Instructor’s manual

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Image bank

The Image Bank provides adopting tutors and lecturers with PDF versions of the figures from the book that may be used in lecture slides and class presentations To access this material please visit http://books.elsevier.com/manuals and follow the instructions on screen

The CES EduPack

CES EduPack is the software-based package to accompany this book, developed by Michael Ashby and Granta Design Used together, Materials Selection in Mechanical Designand CES EduPack provide a complete materials, manufacturing and design course For further information please see the last page of this book, or visit www.grantadesign.com

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Preface xi

Acknowledgements xii

Features of the Third Edition xiii

1 Introduction

1.1 Introduction and synopsis

1.2 Materials in design

1.3 The evolution of engineering materials

1.4 Case study: the evolution of materials in vacuum cleaners

1.5 Summary and conclusions

1.6 Further reading

2 The design process 11

2.1 Introduction and synopsis 12

2.2 The design process 12

2.3 Types of design 16

2.4 Design tools and materials data 17

2.5 Function, material, shape, and process 19

2.6 Case study: devices to open corked bottles 20

2.7 Summary and conclusions 24

2.8 Further reading 25

3 Engineering materials and their properties 27

3.2 The families of engineering materials 28

3.3 The definitions of material properties 30

4 Material property charts 45

4.2 Exploring material properties 46

4.3 The material property charts 50

5 Materials selection — the basics 79

5.2 The selection strategy 81

5.3 Attribute limits and material indices 85

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5.5 Computer-aided selection 99

5.6 The structural index 102

6 Materials selection — case studies 105

6.2 Materials for oars 106

6.3 Mirrors for large telescopes 110

6.4 Materials for table legs 114

6.5 Cost: structural material for buildings 117

6.6 Materials for flywheels 121

6.7 Materials for springs 126

6.8 Elastic hinges and couplings 130

6.9 Materials for seals 133

6.10 Deflection-limited design with brittle polymers 136

6.11 Safe pressure vessels 140

6.12 Stiff, high damping materials for shaker tables 144

6.13 Insulation for short-term isothermal containers 147

6.14 Energy-efficient kiln walls 151

6.15 Materials for passive solar heating 154

6.16 Materials to minimize thermal distortion in precision devices 157

6.17 Nylon bearings for ships’ rudders 160

6.18 Materials for heat exchangers 163

6.19 Materials for radomes 168

7 Processes and process selection 175

7.2 Classifying processes 177

7.3 The processes: shaping, joining, and finishing 180

7.4 Systematic process selection 195

7.5 Ranking: process cost 202

7.6 Computer-aided process selection 209

7.7 Supporting information 215

8 Process selection case studies 219

8.2 Forming a fan 220

8.3 Fabricating a pressure vessel 223

8.4 An optical table 227

8.5 Economical casting 230

8.6 Computer-based selection: a manifold jacket 232

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8.7 Computer-based selection: a spark-plug insulator 235

9 Multiple constraints and objectives 239

9.2 Selection with multiple constraints 241

9.3 Conflicting objectives, penalty-functions, and exchange constants 245

Appendix: Traditional methods of dealing with multiple constraints 256 and objectives

10 Case studies — multiple constraints and conflicting objectives 261

10.2 Multiple constraints: con-rods for high-performance engines 262

10.3 Multiple constraints: windings for high-field magnets 266

10.4 Conflicting objectives: casings for a mini-disk player 272

10.5 Conflicting objectives: materials for a disk-brake caliper 276

11 Selection of material and shape 283

11.2 Shape factors 285

11.3 Microscopic or micro-structural shape factors 296

11.4 Limits to shape efficiency 301

11.5 Exploring and comparing structural sections 305

11.6 Material indices that include shape 307

11.7 Co-selecting material and shape 312

12 Selection of material and shape: case studies 317

12.2 Spars for man-powered planes 319

12.3 Ultra-efficient springs 322

12.4 Forks for a racing bicycle 326

12.5 Floor joists: wood, bamboo or steel? 328

12.6 Increasing the stiffness of steel sheet 331

12.7 Table legs again: thin or light? 333

12.8 Shapes that flex: leaf and strand structures 335

13 Designing hybrid materials 339

13.2 Filling holes in material-property space 342

13.3 The method: AỵBỵconfigurationỵscale 346

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13.5 Sandwich structures: hybrids of type 358

13.6 Lattices: hybrids of type 363

13.7 Segmented structures: hybrids of type 371

14 Hybrid case studies 379

14.2 Designing metal matrix composites 380

14.3 Refrigerator walls 382

14.4 Connectors that not relax their grip 384

14.5 Extreme combinations of thermal and electrical conduction 386

14.6 Materials for microwave-transparent enclosures 389

14.7 Exploiting anisotropy: heat spreading surfaces 391

14.8 The mechanical efficiency of natural materials 393

14.9 Further reading: natural materials 399

15 Information and knowledge sources for design 401

15.2 Information for materials and processes 403

15.3 Screening information: structure and sources 407

15.4 Supporting information: structure and sources 409

15.5 Ways of checking and estimating data 411

16 Materials and the environment 417

16.2 The material life cycle 418

16.3 Material and energy-consuming systems 419

16.4 The eco-attributes of materials 422

16.5 Eco-selection 427

16.6 Case studies: drink containers and crash barriers 433

17 Materials and industrial design 439

17.2 The requirements pyramid 440

17.3 Product character 442

17.4 Using materials and processes to create product personality 445

18 Forces for change 457

18.2 Market-pull and science-push 458

18.3 Growing population and wealth, and market saturation 464

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18.4 Product liability and service provision 465

18.5 Miniaturization and multi-functionality 466

18.6 Concern for the environment and for the individual 467

Appendix A Useful solutions to standard problems 471

Introduction and synopsis 473

A.1 Constitutive equations for mechanical response 474

A.2 Moments of sections 476

A.3 Elastic bending of beams 478

A.4 Failure of beams and panels 480

A.5 Buckling of columns, plates, and shells 482

A.6 Torsion of shafts 484

A.7 Static and spinning disks 486

A.8 Contact stresses 488

A.9 Estimates for stress concentrations 490

A.10 Sharp cracks 492

A.11 Pressure vessels 494

A.12 Vibrating beams, tubes, and disks 496

A.13 Creep and creep fracture 498

A.14 Flow of heat and matter 500

A.15 Solutions for diffusion equations 502

A.16 Further reading 504

Appendix B Material indices 507

B.1 Introduction and synopsis 508

B.2 Use of material indices 508

Appendix C Data and information for engineering materials 513

C.1 Names and applications: metals and alloys 514

C.2 Names and applications: polymers and foams 515

C.3 Names and applications: composites, ceramics, glasses, and

natural materials 516

C.4 Melting temperature,Tm, and glass temperature,Tg 518

C.5 Density, 520

C.6 Young’s modulus,E 522

C.7 Yield strength,y, and tensile strength, ts 524

C.8 Fracture toughness (plane-strain),K1C 526

C.9 Thermal conductivity, 528

C.10 Thermal expansion, 530

C.11 Approximate production energies and CO2burden 532

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Appendix D Information and knowledge sources for materials and processes 537

D.1 Introduction 538

D.2 Information sources for materials 538

D.3 Information for manufacturing processes 552

D.4 Databases and expert systems in software 553

D.5 Additional useful internet sites 554

D.6 Supplier registers, government organizations, standards and

professional societies 555

Appendix E Exercises 557

E.1 Introduction to the exercises 558

E.2 Devising concepts 559

E.3 Use of material selection charts 559

E.4 Translation: constraints and objectives 562

E.5 Deriving and using material indices 565

E.6 Selecting processes 574

E.7 Multiple constraints and objectives 579

E.8 Selecting material and shape 587

E.9 Hybrid materials 594

Index 599

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5000BC

10000BC 1000 1500 1800 1900 1940 1960 1980 1990 2000 2010 2020 5000BC

10000BC 1000 1500 1800 1900 1940 1960 1980 1990 2000 2010 2020 Gold

Gold CopperCopper Bronze Bronze Iron Iron Cast Iron Cast Iron Wood Wood Skins Skins Fibres

Fibres GluesGlues

Rubber Rubber Straw-Brick

Straw-Brick PaperPaper

Bakerlite Bakerlite Stone Stone Flint Flint Pottery Pottery Glass Glass Cement Cement Refractories Refractories Portland Portland Cement Cement FusedFused

Silica

Silica CeramicsCeramicsPyro- Pyro-Steels Steels Alloy Alloy Steels Steels Light Light Alloys Alloys Super Alloys Super Alloys Titanium Titanium Zirconium Zirconium AlloysAlloys etc

etc

Nylon Nylon PE

PE PMMAPMMA AcrylicsAcrylics PC

PC PSPS PPPP Cermets Cermets Epoxies Epoxies Polyesters Polyesters Tough Engineering Tough Engineering Ceramics ( Al

Ceramics ( Al2O3, Si, Si3N4, PSZ etc ), PSZ etc ) GFRP

GFRPCFRPCFRP Kelvar-FRP Kelvar-FRP

Composites CompositesMetal-MatrixMetal-Matrix

Ceramic Composites Ceramic Composites High Modulus High Modulus Polymers Polymers High Temperature High Temperature Polymers Polymers Development Slow: Development Slow: Mostly Quality Mostly Quality Control and Control and Processing Processing Glassy Metals Glassy Metals Al-Lithium Alloys Al-Lithium Alloys Dual Phase Steels Dual Phase Steels Microalloyed Steels Microalloyed Steels New Super Alloys New Super Alloys Gold Copper Bronze Iron Cast Iron Wood Skins Fibres Glues Rubber Straw-Brick Paper Bakerlite Stone Flint Pottery Glass Cement Refractories Portland Cement Fused

Silica Ceramics Pyro-Steels Alloy Steels Light Alloys Super Alloys Titanium Zirconium Alloys etc Nylon

PE PMMA Acrylics PC PS PP

Cermets

Epoxies Polyesters

Tough Engineering

Ceramics ( Al2O3, Si3N4, PSZ etc )

GFRPCFRP Kelvar-FRP CompositesMetal-Matrix Ceramic Composites High Modulus Polymers High Temperature Polymers Development Slow: Mostly Quality Control and Processing Glassy Metals Al-Lithium Alloys Dual Phase Steels Microalloyed Steels New Super Alloys

DATE Relative importance Polymers & elastomers Polymers & elastomers Composites Composites Ceramics & glasses Ceramics & glasses Metals Metals Chapter contents

1.4 Case study: the evolution of materials in

vacuum cleaners

1.6 Further reading

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‘‘Design’’ is one of those words that means all things to all people Every manufactured thing, from the most lyrical of ladies’ hats to the greasiest of gearboxes, qualifies, in some sense or other, as a design It can mean yet more Nature, to some, is Divine Design; to others it is design by Natural Selection The reader will agree that it is necessary to narrow the field, at least a little

This book is about mechanical design, and the role of materials in it Mechanical components have mass; they carry loads; they conduct heat and electricity; they are exposed to wear and to corrosive environments; they are made of one or more materials; they have shape; and they must be manu-factured The book describes how these activities are related

Materials have limited design since man first made clothes, built shelters, and waged wars They still But materials and processes to shape them are developing faster now than at any previous time in history; the challenges and opportunities they present are greater than ever before The book develops a strategy for confronting the challenges and seizing the opportunities

Design is the process of translating a new idea or a market need into the detailed information from which a product can be manufactured Each of its stages requires decisions about the materials of which the product is to be made and the process for making it Normally, the choice of material is dictated by the design But sometimes it is the other way round: the new product, or the evolution of the existing one, was suggested or made possible by the new material The number of materials available to the engineer is vast: something over 120,000 are at his or her (from here on ‘‘his’’ means both) disposal And although standardization strives to reduce the number, the continuing appearance of new materials with novel, exploitable, properties expands the options further

How, then, does the engineer choose, from this vast menu, the material best suited to his purpose? Must he rely on experience? In the past he did, passing on this precious commodity to apprentices who, much later in their lives, might assume his role as the in-house materials guru who knows all about the things the company makes But many things have changed in the world of engineering design, and all of them work against the success of this model There is the drawn-out time scale of apprentice-based learning There is job mobility, meaning that the guru who is here today is gone tomorrow And there is the rapid evolution of materials information, already mentioned

There is no question of the value of experience But a strategy relying on experience-based learning is not in tune with the pace and re-dispersion of talent that is part of the age of information technology We need asystematic

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procedure — one with steps that can be taught quickly, that is robust in the decisions it reaches, that allows of computer implementation, and with the ability to interface with the other established tools of engineering design The question has to be addressed at a number of levels, corresponding to the stage the design has reached At the beginning the design is fluid and the options are wide; all materials must be considered As the design becomes more focused and takes shape, the selection criteria sharpen and the short-list of materials that can satisfy them narrows Then more accurate data are required (though for a lesser number of materials) and a different way of analyzing the choice must be used In the final stages of design, precise data are needed, but for still fewer materials — perhaps only one The procedure must recognize the initial richness of choice, and at the same time provide the precision and detail on which final design calculations can be based

The choice of material cannot be made independently of the choice of process by which the material is to be formed, joined, finished, and otherwise treated Cost enters, both in the choice of material and in the way the material is processed So, too, does the influence material usage on the environment in which we live And it must be recognized that good engineering design alone is not enough to sell products In almost everything from home appliances through automobiles to aircraft, the form, texture, feel, color, decoration of the product — the satisfaction it gives the person who owns or uses it — are important This aspect, known confusingly as ‘‘industrial design’’, is one that, if neglected, can lose the manufacturer his market Good designs work; excellent designs also give pleasure

Design problems, almost always, are open-ended They not have a unique or ‘‘correct’’ solution, though some solutions will clearly be better than others They differ from the analytical problems used in teaching mechanics, or structures, or thermodynamics, which generally have single, correct answers So the first tool a designer needs is an open mind: the willingness to consider all possibilities But a net cast widely draws in many fish A procedure is necessary for selecting the excellent from the merely good

This book deals with the materials aspects of the design process It develops a methodology that, properly applied, gives guidance through the forest of complex choices the designer faces The ideas ofmaterial and process attributes

are introduced They are mapped on material and process selection charts

that show the lay of the land, so to speak, and simplify the initial survey for potential candidate-materials Real life always involves conflicting objectives— minimizing mass while at the same time minimizing cost is an example — requiring the use of trade-off methods The interaction between

material and shapecan be built into the method Taken together, these suggest schemes for expanding the boundaries of material performance by creating

hybrids— combinations of two or more materials, shapes and configurations with unique property profiles None of this can be implemented withoutdata

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change in the materials-world are surveyed, the most obvious of which is that dealing with environmental concerns The appendices contain useful information

The methods lend themselves readily to implementation as computer-based tools; one,The CES materials and process selection platform,1has been used for the case studies and many of the figures in this book They offer, too, potential for interfacing with other computer-aided design, function modeling, optimization routines, but this degree of integration, though under develop-ment, is not yet commercially available

All this will be found in the following chapters, with case studies illustrating applications But first, a little history

Throughout history, materials have limited design The ages in which man has lived are named for the materials he used: stone, bronze, iron And when he died, the materials he treasured were buried with him: Tutankhamen in his enameled sarcophagus, Agamemnon with his bronze sword and mask of gold, each representing the high technology of their day

If they had lived and died today, what would they have taken with them? Their titanium watch, perhaps; their carbon-fiber reinforced tennis racquet, their metal-matrix composite mountain bike, their shape-memory alloy eye-glass frames with diamond-like carbon coated lenses, their polyether– ethyl–ketone crash helmet This is not the age of one material, it is the age of an immense range of materials There has never been an era in which their evolution was faster and the range of their properties more varied The menu of materials has expanded so rapidly that designers who left college 20 years ago can be forgiven for not knowing that half of them exist But not-to-know is, for the designer, to risk disaster Innovative design, often, means the imaginative exploitation of the properties offered by new or improved materials And for the man in the street, the schoolboy even, not-to-know is to miss one of the great developments of our age: the age of advanced materials

This evolution and its increasing pace are illustrated in Figure 1.1 The materials of pre-history (>10,000 BC, the Stone Age) were ceramics and glasses, natural polymers, and composites Weapons — always the peak of technology — were made of wood and flint; buildings and bridges of stone and wood Naturally occurring gold and silver were available locally and, through their rarity, assumed great influence as currency, but their role in technology was small The development of rudimentary thermo-chemistry allowed the

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extraction of, first, copper and bronze, then iron (the Bronze Age, 4000–1000 BC and the Iron Age, 1000 BC–1620 AD) stimulating enormous advances, in technology (There is a cartoon on my office door, put there by a student, showing an aggrieved Celt confronting a sword-smith with the words: ‘‘You sold me this bronze sword last week and now I’m supposed to upgrade to iron!’’) Cast iron technology (1620s) established the dominance of metals in engineering; and since then the evolution of steels (1850 onward), light alloys (1940s) and special alloys, has consolidated their position By the 1960s, ‘‘engineering materials’’ meant ‘‘metals’’ Engineers were given courses in metallurgy; other materials were barely mentioned

There had, of course, been developments in the other classes of material Improved cements, refractories, and glasses, and rubber, bakelite, and poly-ethylene among polymers, but their share of the total materials market was small Since 1960 all that has changed The rate of development of new metallic alloys is now slow; demand for steel and cast iron has in some countries

5000BC

10000BC 1000 1500 1800 1900 1940 1960 1980 1990 2000 2010 2020

5000BC

10000BC 1000 1500 1800 1900 1940 1960 1980 1990 2000 2010 2020

Gold

Gold CopperCopper Bronze Bronze Iron Iron Cast Iron Cast Iron Wood Wood Skins Skins Fibres

Fibres GluesGlues

Rubber Rubber

Straw-Brick Straw-Brick PaperPaper

Bakerlite Bakerlite Stone Stone Flint Flint Pottery Pottery Glass Glass Cement Cement Refractories Refractories Portland Portland Cement Cement FusedFused

Silica

Silica CeramicsCeramicsPyro- Pyro-Steels Steels Alloy Alloy Steels Steels Light Light Alloys Alloys Super Alloys Super Alloys Titanium Titanium Zirconium Zirconium AlloysAlloys etc

etc

Nylon Nylon PE

PE PMMAPMMA AcrylicsAcrylics PC

PC PSPS PPPP

Cermets Cermets Epoxies Epoxies Polyesters Polyesters Tough Engineering Tough Engineering Ceramics ( Al

Ceramics ( Al2O3, Si, Si3N4, PSZ etc ), PSZ etc ) GFRP

GFRPCFRPCFRP Kelvar-FRP Kelvar-FRP

Composites CompositesMetal-MatrixMetal-Matrix

Ceramic Composites Ceramic Composites High Modulus High Modulus Polymers Polymers High Temperature High Temperature Polymers Polymers Development Slow: Development Slow: Mostly Quality Mostly Quality Control and Control and Processing Processing Glassy Metals Glassy Metals Al-Lithium Alloys Al-Lithium Alloys Dual Phase Steels Dual Phase Steels

Microalloyed Steels Microalloyed Steels New Super Alloys New Super Alloys

Gold Copper Bronze Iron Cast Iron Wood Skins Fibers Glues Rubber Straw-Brick Paper Bakelite Stone Flint Pottery Glass Cement Refractories Portland Cement Fused

Silica Ceramics Pyro-Steels Alloy Steels Light Alloys Super Alloys Titanium Zirconium Alloys etc Nylon

PE PMMA Acrylics PC PS PP

Cermets

Epoxies Polyesters

Tough Engineering

Ceramics ( Al2O3, Si3N4, PSZ etc.)

GFRPCFRP Kelvar-FRP CompositesMetal-Matrix Ceramic Composites High Modulus Polymers High Temperature Polymers Development Slow: Mostly Quality Control and Processing Glassy Metals Al-Lithium Alloys Dual Phase Steels Microalloyed Steels New Super Alloys

DATE Relative importance Polymers & elastomers Polymers & elastomers Composites Composites Ceramics & glasses Ceramics & glasses Metals Metals

Figure 1.1 The evolution of engineering materials with time ‘‘Relative importance’’ is based on

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actually fallen.2 The polymer and composite industries, on the other hand,

are growing rapidly, and projections of the growth of production of the new high-performance ceramics suggests continued expansion here also

This rapid rate of change offers opportunities that the designer cannot afford to ignore The following case study is an example

1.4 Case study: the evolution of materials in vacuum cleaners

Sweeping and dusting are homicidal practices: they consist of taking dust from the floor, mixing it in the atmosphere, and causing it to be inhaled by the inhabitants of the house In reality it would be preferable to leave the dust alone where it was

That was a doctor, writing about 100 years ago More than any previous generation, the Victorians and their contemporaries in other countries worried about dust They were convinced that it carried disease and that dusting merely dispersed it when, as the doctor said, it became yet more infectious Little wonder, then, that they invented the vacuum cleaner

The vacuum cleaners of 1900 and before were human-powered (Figure 1.2(a)) The housemaid, standing firmly on the flat base, pumped the handle of the cleaner, compressing bellows that, via leather flap-valves to give a one-way flow, sucked air through a metal can containing the filter at a flow rate of about l/s The butler manipulated the hose The materials are, by today’s standards, pri-mitive: the cleaner is made almost entirely from natural materials: wood, canvas, leather and rubber The only metal is the straps that link the bellows (soft iron) and the can containing the filter (mild steel sheet, rolled to make a cylinder) It reflects the use of materials in 1900 Even a car, in 1900, was mostly made of wood, leather, and rubber; only the engine and drive train had to be metal

The electric vacuum cleaner first appeared around 1908.3By 1950 the design had evolved into the cylinder cleaner shown in Figure 1.2(b) (flow rate about 10 l/s) Air flow is axial, drawn through the cylinder by an electric fan The fan occupies about half the length of the cylinder; the rest holds the filter One advance in design is, of course, the electrically driven air pump The motor, it is true, is bulky and of low power, but it can function continuously without tea breaks or housemaid’s elbow But there are others: this cleaner is almost entirely made of metal: the case, the end-caps, the runners, even the tube to suck up the dust are mild steel: metals have entirely replaced natural materials Developments since then have been rapid, driven by the innovative use of new materials The 1985 vacuum cleaner of Figure 1.2(c) has the power of roughly 16 housemaids working flat out (800 W) and a corresponding air

Do not, however, imagine that the days of steel are over Steel production accounts for 90% of all world metal output, and its unique combination of strength, ductility, toughness, and low price makes steel irreplaceable

3

Inventors: Murray Spengler and William B Hoover The second name has become part of the English language, along with those of such luminaries as John B Stetson (the hat), S.F.B Morse (the code), Leo Henrik Baikeland (Bakelite), and Thomas Crapper (the flush toilet)

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flow-rate; cleaners with twice that power are now available Air flow is still axial and dust-removal by filtration, but the unit is smaller than the old cylinder cleaners This is made possible by a higher power-density in the motor, reflecting better magnetic materials, and higher operating temperatures (heat-resistant insulation, windings, and bearings) The casing is entirely polymeric, and is an example of good design with plastics The upper part is a single molding, with all additional bits attached by snap fasteners molded into the original component No metal is visible anywhere; even the straight part of the suction tube, metal in all earlier models, is now polypropylene The number of components is dramatically reduced: the casing has just parts, held together by just fastener, compared with 11 parts and 28 fasteners for the 1950 cleaner The saving on weight and cost is enormous, as the comparison in Table 1.1 shows It is arguable that this design (and its many variants) is near-optimal for today’s needs; that a change of working principle, material or process could increase performance but at a cost-penalty unacceptable to the consumer We will leave the discussion of balancing performance against cost to a later chapter, and merely note here that one manufacturer disagrees The cleaner shown in Figure 1.2(d) exploits a different concept: that of inertial separation rather than filtration For this to work, the power and rotation speed have to be high; the product is larger, heavier and more expensive than the competition Yet it sells — a testament to good industrial design and imaginative marketing

1905 1950

1985 1997

(a) (b)

(c) (d)

Figure 1.2 Vacuum cleaners: (a) the hand-powered bellows cleaner of 1900, largely made of wood

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All this has happened within one lifetime Competitive design requires the innovative use of new materials and the clever exploitation of their special properties, both engineering and aesthetic Many manufacturers of vacuum cleaners failed to innovate and exploit; now they are extinct That sombre thought prepares us for the chapters that follow in which we consider what they forgot: the optimum use of materials in design

The number of engineering materials is large: tens of thousands, at a conservative estimate The designer must select, from this vast menu, the few best suited to his task This, without guidance, can be a difficult and haphazard business, so there is a temptation to choose the material that is ‘‘traditional’’ for the application: glass for bottles; steel cans That choice may be safely con-servative, but it rejects the opportunity for innovation Engineering materials are evolving faster, and the choice is wider than ever before Examples of products in which a new material has captured a market are as common as — well — as plastic bottles Or aluminium cans Or polycarbonate eyeglass lenses Or carbon-fiber golf club shafts It is important in the early stage of design, or of re-design, to examine the full materials menu, not rejecting options merely because they are unfamiliar That is what this book is about

1.6 Further reading

The history and evolution of materials

A History of Technology(21 volumes), edited by Singer, C., Holmyard, E.J., Hall, A.R., Williams, T.I., and Hollister-Short, G Oxford University Press (1954–2001)

Table 1.1 Comparison of cost, power, and weight of vacuum cleaners

Cleaner and date

Dominant materials

Power (W)

Weight (kg)

Approximate cost* Hand powered,

1900

Wood, canvas, leather

50 10 £240–$380

Cylinder, 1950 Mild steel 300 £96–$150

Cylinder, 1985 Molded ABS and polypropylene

800 £60–$95

Dyson, 1995 Polypropylene, polycarbonate, ABS

1200 6.3 £190–$300

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Oxford, UK ISSN 0307–5451.(A compilation of essays on aspects of technology, including materials.)

Delmonte, J (1985)Origins of Materials and Processes, Technomic Publishing Com-pany, Pennsylvania, USA ISBN 87762-420-8 (A compendium of information on when materials were first used, any by whom.)

Dowson, D (1998) History of Tribology, Professional Engineering Publishing Ltd., London, UK ISBN 1-86058-070-X (A monumental work detailing the history of devices limited by friction and wear, and the development of an understanding of these phenomena.)

Emsley, J (1998),Molecules at an Exhibition, Oxford University Press, Oxford, UK ISBN 0-19-286206-5 (Popular science writing at its best: intelligible, accurate, simple and clear The book is exceptional for its range The message is that molecules, often meaning materials, influence our health, our lives, the things we make and the things we use.)

Michaelis, R.R (1992) editor ‘‘Gold: art, science and technology’’, and ‘‘Focus on gold’’, Interdisciplinary Science Reviews, volume 17 numbers and 4.ISSN 0308–0188 (A comprehensive survey of the history, mystique, associations and uses of gold.) The Encyclopaedia Britannica, 11th edition (1910) The Encyclopaedia Britannica

Company, New York, USA.(Connoisseurs will tell you that in its 11th edition the Encyclopaedia Britannica reached a peak of excellence which has not since been equalled, though subsequent editions are still usable.)

Tylecoate, R.F (1992)A History of Metallurgy, 2nd edition, The Institute of Materials, London, UK ISBN 0-904357-066.(A total-immersion course in the history of the extraction and use of metals from 6000BC to 1976, told by an author with forensic talent and love of detail.)

And on vacuum cleaners

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Data for ALL materials, low precision

and detail

Data for a SUBSET of materials, higher precision and detail

Data for ONE material, highest precision

and detail Function modelling

Viabiliey studies Approximate analysis Geometric modelling Simulations methods

Cost modelling Componenet modelling

Finite-element modelling (FEM)

DFM, DFA

Market need: design requirements

Product specification Embodiment

Detail Concept

Material data needs Design tools

Chapter contents

2.2 The design process 12

2.3 Types of design 16

2.4 Design tools and materials data 17 2.5 Function, material, shape, and process 19 2.6 Case study: devices to open

corked bottles 20

Chapter 2

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It ismechanical designwith which we are primarily concerned here; it deals with the physical principles, the proper functioning and the production of mechanical systems This does not mean that we ignore industrial design, which speaks of pattern, color, texture, and (above all) consumer appeal — but that comes later The starting point is good mechanical design, and the ways in which the selection of materials and processes contribute to it

Our aim is to develop a methodology for selecting materials and processes that isdesign-led; that is, the selection uses, as inputs, the functional require-ments of the design To so we must first look briefly at design itself Like most technical fields it is encrusted with its own special jargon, some of it bordering on the incomprehensible We need very little, but it cannot all be avoided This chapter introduces some of the words and phrases — the vocabulary — of design, the stages in its implementation, and the ways in which materials selection links with these

2.2 The design process

The starting point is amarket need or a new idea; the end point is the full

product specification of a product that fills the need or embodies the idea A need must be identified before it can be met It is essential to define the need precisely, that is, to formulate aneed statement, often in the form: ‘‘a device is required to perform task X’’, expressed as a set ofdesign requirements Writers on design emphasize that the statement and its elaboration in the design requirements should be solution-neutral(i.e they should not imply how the task will be done), to avoid narrow thinking limited by pre-conceptions Between the need statement and the product specification lie the set of stages shown in Figure 2.1: the stages of conceptual, embodiment and detailed designs, explained in a moment

The product itself is called atechnical system A technical system consists of

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which performs a specific function, as in Figure 2.3; the resulting arrangement is called the function-structureorfunction decompositionof the system It is like describing a cat as an appropriate linkage of a respiratory system, a cardio-vascular system, a nervous system, a digestive system and so on Alternative designs link the unit functions in alternative ways, combine functions, or split them The function-structure gives a systematic way of assessing design options

The design proceeds by developing concepts to perform the functions in the function structure, each based on aworking principle At this, the conceptual design stage, all options are open: the designer considers alternative concepts and the ways in which these might be separated or combined The next stage, embodiment, takes the promising concepts and seeks to analyze their operation at an approximate level This involves sizing the components, and selecting materials that will perform properly in the ranges of stress, temperature, and environment suggested by the design requirements, examining the implications for performance and cost The embodiment stage ends with a feasible layout, which is then passed to the detailed design stage Here specifications for each

Develop layout, scale, form Model and analyze assemblies Optimize the functions Evaluate and select layouts

Analyze components in detail Final choice of material and process Opimize performance and cost Prepare detailed drawings

Product

specification Iterate

Define specification Determine function structure Seek working principles Evaluate and select concepts

Embodiment

Figure 2.1 The design flow chart The design proceeds from the identification of amarket need, clarified as a set ofdesign requirements, throughconcept, embodimentanddetailedanalysis to a

product specification

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Technical system

Sub-assembly

Component 1.1

Component 1.2

Component 1.3

Sub-assembly

Component 2.1

Component 2.2

Component 2.3

Component 3.1

Component 3.2

Component 3.3

Figure 2.2 The analysis of a technical system as a breakdown into assemblies and components Material and process selection is at the component level

Energy Material Information

Function

Inputs

Function

Technical system

Outputs

Sub-systems

Function

Energy Material Information

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component are drawn up Critical components may be subjected to precise mechanical or thermal analysis Optimization methods are applied to com-ponents and groups of comcom-ponents to maximize performance A final choice of geometry and material is made and the methods of production are analyzed and costed The stage ends with a detailed production specification

All that sounds well and good If only it were so simple The linear process suggested by Figure 2.1 obscures the strong coupling between the three stages The consequences of choices made at the concept or embodiment stages may not become apparent until the detail is examined Iteration, looping back to explore alternatives, is an essential part of the design process Think of each of the many possible choices that couldbe made as an array of blobs in design space as suggested by Figure 2.4 Here C1, C2, .are possible concepts, and E1, E2, ., and D1, D2, are possible embodiments and detailed

Product specification C1

C2 C6

C4 C7 C3

E3 C5

E1 E6

E2 E4

E7 E8

D3

E5

D2 D1

D4

D6 D5 Embodiment

Figure 2.4 The previous figure suggests that the design process is logical and linear The reality is otherwise Here the C-blobs represent possible concepts, the E-blobs possible embodiments of the Cs, and the D-blobs possible detailed realizations of the Es The process is complete when a compatible path form ‘‘Need’’ to ‘‘Specification’’ can be identified The extreme coupling between the idealized design ‘‘stages’’ leads to a devious path (the full line) and many dead-ends (the broken lines) This creates the need for tools that allow fluid access to materials information at differing levels of breadth and detail

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elaborations of them Then the design process becomes one of creating paths, linking compatible blobs, until a connection is made from the top (‘‘market need’’) to the bottom (‘‘product specification’’) The trial paths have dead-ends, and they loop back It is like finding a track across difficult terrain — it may be necessary to go back many times if, in the end, we are to go forward Once a path is found, it is always possible to make it look linear and logical (and many books this), but the reality is more like Figure 2.4, not Figure 2.1 Thus a key part of design, and of selecting materials for it, is flexibility, the ability to explore alternatives quickly, keeping the big picture as well as the details in focus Our focus in later chapters is on the selection of materials and processes, where exactly the same need arises This requires simple mappings of the ‘‘kingdoms’’ of materials and processes that allow quick surveys of alternatives while still providing detail when it is needed The selection charts of Chapter and the methods of Chapter help this

Described in the abstract, these ideas are not easy to grasp An example will help — it comes in Section 2.6 First, a look at types of design

2.3 Types of design

It is not always necessary to start, as it were, from scratch Original design

does: it involves a new idea or working principle (the ball-point pen, the compact disc) New materials can offer new, unique combinations of proper-ties that enable original design Thus high-purity silicon enabled the transistor; high-purity glass, the optical fiber; high coercive-force magnets, the miniature earphone, solid-state lasers the compact disc Sometimes the new material suggests the new product; sometimes instead the new product demands the development of a new material: nuclear technology drove the development of a series of new zirconium-based alloys and low-carbon stainless steels; space technology stimulated the development of light-weight composites; turbine technology today drives development of high-temperature alloys and ceramics

Adaptive or developmental designtakes an existing concept and seeks an incremental advance in performance through a refinement of the working principle This, too, is often made possible by developments in materials: polymers replacing metals in household appliances; carbon fiber replacing wood in sports goods The appliance and the sports-goods market are both large and competitive Markets here have frequently been won (and lost) by the way in which the manufacturer has adapted the product by exploiting new materials

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steel; subsonic planes are made of one alloy, supersonic of another; and for good reasons, detailed in later chapters

2.4 Design tools and materials data

To implement the steps of Figure 2.1, use is made of design tools They are shown as inputs, attached to the left of the main backbone of the design methodology in Figure 2.5 The tools enable the modeling and optimization of a design, easing the routine aspects of each phase Function-modelers suggest viable function structures Configuration optimizers suggest or refine shapes Geometric and 3D solid modeling packages allow visualization and create files that can be down-loaded to numerically controlled prototyping and manufacturing systems Optimization, DFM, DFA,1and cost-estimation

Data for ALL materials, low precision

and detail

Data for a SUBSET of materials, higher precision and detail

Data for ONE material, highest precision

and detail Function modeling

Viability studies

Approximate analysis

Geometric modeling

Simulations methods

Cost modeling

Component modeling Finite-element modeling (FEM)

DFM, DFA

Product specification Embodiment

Material data needs Design tools

Figure 2.5 The design flow chart, showing how design tools and materials selection enter the procedure Information about materials is needed at each stage, but at very different levels of breadth and precision

1 Design for Manufacture and Design for Assembly.

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software allows manufacturing aspects to be refined Finite element (FE) and Computational Fluid Dynamics (CFD) packages allow precise mechanical and thermal analysis even when the geometry is complex and the deformations are large There is a natural progression in the use of the tools as the design evolves: approximate analysis and modeling at the conceptual stage; more sophisticated modeling and optimization at the embodiment stage; and precise (‘‘exact’’ —

but nothing is ever that) analysis at the detailed design stage

Materials selection enters each stage of the design The nature of the data needed in the early stages differs greatly in its level of precision and breadth from that needed later on (Figure 2.5, right-hand side) At the concept-stage, the designer requires approximate property-values, but for the widest possible range of materials All options are open: a polymer may be the best choice for one concept, a metal for another, even though the function is the same The problem, at this stage, is not precision and detail; it is breadth and speed of access: how can the vast range of data be presented to give the designer the greatest freedom in considering alternatives?

At the embodiment stage the landscape has narrowed Here we need data for a subset of materials, but at a higher level of precision and detail These are found in the more specialized handbooks and software that deal with a single class or sub-class of materials — metals, or just aluminum alloys, for instance The risk now is that of loosing sight of the bigger spread of materials to which we must return if the details not work out; it is easy to get trapped in a single line of thinking — a single set of ‘‘connections’’ in the sense described in the last section — when other combinations of connections offer a better solution to the design problem

The final stage of detailed design requires a still higher level of precision and detail, but for only one or a very few materials Such information is best found in the data-sheets issued by the material producers themselves, and in detailed databases for restricted material classes A given material (polyethylene, for instance) has a range of properties that derive from differences in the ways different producers make it At the detailed design stage, a supplier must be identified, and the properties of his product used in the design calculations; that from another supplier may have slightly different properties And sometimes even this is not good enough If the component is a critical one (meaning that its failure could, in some sense or another, be disastrous) then it may be pru-dent to conduct in-house tests to measure the critical properties, using a sample of the material that will be used to make the product itself

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views of enthusiasts, and try out candidate-bikes yourself And if you not like them you go back one or more steps Only when a match between your need and an available product is found you make a final selection

The materials input does not end with the establishment of production Products fail in service, and failures contain information It is an imprudent manufacturer who does not collect and analyze data on failures Often this points to the misuse of a material, one that redesign or re-selection can eliminate

2.5 Function, material, shape, and process

The selection of a material and process cannot be separated from the choice of shape We use the word ‘‘shape’’ to include the external,macro-shape, and — when necessary — the internal, ormicro-shape, as in a honeycomb or cellular structure To make the shape, the material is subjected to processes that, col-lectively, we shall call manufacture: they include primary forming processes (like casting and forging), material removal processes (machining, drilling), finishing processes (such as polishing) and joining processes (e.g welding) Function, material, shape and process interact (Figure 2.6) Function dictates the choice of both material and shape Process is influenced by the material: by its formability, machinability, weldability, heat-treatability, and so on Process obviously interacts with shape — the process determines the shape, the size, the precision and, of course, the cost The interactions are two-way: specifi-cation of shape restricts the choice of material and process; but equally the

Function

Material

Process

Shape

Figure 2.6 The central problem of materials selection in mechanical design: the interaction between function, material, shape and process

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specification of process limits the materials you can use and the shapes they can take The more sophisticated the design, the tighter the specifications and the greater the interactions It is like making wine: to make cooking wine, almost any grape and fermentation process will do; to make champagne, both grape and process must be tightly constrained

The interaction between function, material, shape, and process lies at the heart of the material selection process But first, a case study to illustrate the design process

2.6 Case study: devices to open corked bottles

Wine, like cheese, is one of man’s improvements on nature And ever since man has cared about wine, he has cared about cork to keep it safely sealed in flasks and bottles ‘‘Corticum .demovebit amphorae .’’ — ‘‘Uncork the amphora .’’ sang Horace2(27 BC) to celebrate the anniversary of his miraculous escape from death by a falling tree But how did he it?

A corked bottle creates a market need: it is the need to gain access to the wine inside We might state it thus: ‘‘A device is required to pull corks from wine bottles.’’ But hold on The need must be expressed in solution-neutral form, and this is not The aim is to gain access to the wine; our statement implies that this will be done by removing the cork, and that it will be removed by pulling There could be other ways So we will try again: ‘‘A device is required to allow access to wine in a corked bottle’’ (Figure 2.7) and one might add, ‘‘with convenience, at modest cost, and without contaminating the wine.’’

?

Figure 2.7 The market need: a device is sought to allow access to wine contained in a corked bottle

2

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Five concepts for doing this are shown in Figure 2.8 In order, they are to remove the cork by axial traction (¼ pulling); to remove it by shear tractions; to push it out from below; to pulverizing it; and to by-pass it altogether — by knocking the neck off the bottle3perhaps

(a) (b)

(d) (e)

(c)

Figure 2.8 Five possible concepts, illustrating physical principles, to fill the need expressed by Figure 2.7

(a) (b) (c)

Figure 2.9 Working principles for implementing the first three schemes of Figure 2.8

3 A Victorian invention for opening old port, the cork of which may become brittle with age and alcohol-absorption, involved ring-shaped tongs The tongs were heated red on an open fire, then clamped onto the cold neck of the bottle The thermal shock removed the neck cleanly and neatly

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Numerous devices exist to achieve the first three of these The others are used too, though generally only in moments of desperation We shall eliminate these on the grounds that they might contaminate the wine, and examine the others more closely, exploring working principles Figure 2.9 shows one for each of

(b) (a)

(d) (c)

(e)

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(a) (b)

(c) (d)

Figure 2.12 Embodiment sketches for four concepts: direct pull, levered pull, geared pull and spring-assisted pull Each system is made up of components that perform a sub-function The requirements of these sub-functions are the inputs to the materials selection method

Direct pull

Levered pull

Geared pull

Direct push

Levered push

Shaft

Linkage

Gas injection

Screw

Shear blades

Gas pressure

Generate

force Transmitforce Apply forceto cork

Figure 2.11 The function structure and working principles of cork removers

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the first three concepts: in the first, a screw is threaded into the cork to which an axial pull is applied; in the second, slender elastic blades inserted down the sides of the cork apply shear tractions when pulled; and in the third the cork is pierced by a hollow needle through which a gas is pumped to push it out

Figure 2.10 shows examples of cork removers using these working princi-ples All are described by the function-structure sketched in the upper part of Figure 2.11: create a force, transmit a force, apply force to cork They differ in the working principle by which these functions are achieved, as indicated in the lower part of the figure The cork removers in the photos combine working principles in the ways shown by the linking lines Others could be devised by making other links

Figure 2.12 shows embodiment sketches for devices based on just one concept — that of axial traction The first is a direct pull; the other three use some sort of mechanical advantage — levered-pull, geared pull and spring-assisted pull; the photos show examples of all of these

The embodiments of Figure 2.9 identify thefunctional requirementsof each component of the device, which might be expressed in statements like:

a cheap screw to transmit a prescribed load to the cork;

a light lever (i.e a beam) to carry a prescribed bending moment;

a slender elastic blade that will not buckle when driven between the cork and bottle-neck;

a thin, hollow needle, stiff and strong enough to penetrate a cork;

and so on The functional requirements of each component are the inputs to the materials selection process They lead directly to the property limits and

material indicesof Chapter 5: they are the first step in optimizing the choice of material to fill a given requirement The procedure developed there takes requirements such as ‘‘light strong beam’’ or ‘‘slender elastic blade’’ and uses them to identify a subset of materials that will perform this function particu-larly well That is what is meant bydesign-led materials selection

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Materials selection enters at each stage, but at different levels of breadth and precision At the conceptual stage all materials and processes are potential can-didates, requiring a procedure that allows rapid access to data for a wide range of each, though without the need for great precision The preliminary selection passes to the embodiment stage, the calculations and optimizations of which require information at a higher level of precision and detail They eliminate all but a small short-list candidate-materials and processes for the final, detailed stage of the design For these few, data of the highest quality are necessary

Data exist at all these levels Each level requires its own data-management scheme, described in the following chapters The management is the skill: it must be design-led, yet must recognize the richness of choice and embrace the complex interaction between the material, its shape, the process by which it is given that shape, and the function it is required to perform And it must allow rapid iteration — back-looping when a particular chain of reasoning proves to be unprofitable Tools now exist to help with all of this We will meet one — the CES materials and process selection platform—later in this book

But given this complexity, why not opt for the safe bet: stick to what you (or others) used before? Many have chosen that option Few are still in business

2.8 Further reading

A chasm exists between books on design methodology and those on materials selection: each largely ignores the other The book by French is remarkable for its insights, but the word ‘material’ does not appear in its index Pahl and Beitz has near-biblical standing in the design camp, but is heavy going Ullman and Cross take a more relaxed approach and are easier to digest The books by Budinski and Budinski, by Charles, Crane and Furness and by Farag present the materials case well, but are less good on design Lewis illustrates material selection through case studies, but does not develop a systematic procedure The best compromise, perhaps, is Dieter

General texts on design methodology

Cross, N (2000) Engineering Design Methods, 3rd edition, Wiley, Chichester, UK ISBN 0-471-87250-4.(A durable text describing the design process, with emphasis on developing and evaluating alternative solutions.)

French, M.J (1985)Conceptual Design for Engineers, The Design Council, London, UK, and Springer, Berlin, Germany ISBN 0-85072-155-5 and 3-540-15175-3.(The origin of the ‘‘Concept — Embodiment — Detail’’ block diagram of the design pro-cess The book focuses on the concept stage, demonstrating how simple physical principles guide the development of solutions to design problems.)

Pahl, G and Beitz, W (1997)Engineering Design, 2nd edition, translated by K Wallace and L Blessing, The Design Council, London, UK and Springer-Verlag, Berlin,

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Germany ISBN 0-85072-124-5 and 3-540-13601-0.(The Bible — or perhaps more exactly the Old Testament — of the technical design field, developing formal methods in the rigorous German tradition.)

Ullman, D.G (1992)The Mechanical Design Process, McGraw-Hill, New York, USA ISBN 0-07-065739-4 (An American view of design, developing ways in which an initially ill-defined problem is tackled in a series of steps, much in the way suggested by Figure 2.1 of the present text.)

Ulrich, K.T and Eppinger, S.D (1995)Product Design and Development, McGraw-Hill, New York, USA ISBN 0-07-065811-0 (A readable, comprehensible text on product design, as taught at MIT Many helpful examples but almost no mention of materials.)

General texts on materials selection in design

Budinski, K.G and Budinski, M.K (1999)Engineering Materials, Properties and Selection 6th edition, Prentice-Hall, Englewood Cliffs, NJ, USA ISBN 0-13-904715-8.(A well-established materials text that deals well with both material properties and pro-cesses.)

Charles, J.A., Crane, F.A.A and Furness, J.A.G (1997) Selection and Use of Engi-neering Materials, 3rd edition, Butterworth-Heinemann Oxford, UK ISBN 0-7506-3277-1.(A materials-science, rather than a design-led, approach to the selection of materials.)

Dieter, G.E (1991) Engineering Design, a Materials and Processing Approach, 2nd edition, McGraw-Hill, New York, USA ISBN 0-07-100829-2.(A well-balanced and respected text focusing on the place of materials and processing in technical design.) Farag, M.M (1989) Selection of Materials and Manufacturing Processes for Engi-neering Design, Prentice-Hall, Englewood Cliffs, NJ, USA ISBN 0-13-575192-6 (Like Charles, Crane and Furness, this is Materials-Science approach to the selection of materials.)

Lewis, G (1990)Selection of Engineering Materials, Prentice-Hall, Englewood Cliffs, N.J., USA ISBN 0-13-802190-2.(A text on materials selection for technical design, based largely on case studies.)

And on corks and corkscrews

McKearin, H (1973) ‘‘On ‘stopping’, bottling and binning’’,International Bottler and Packer, April issue, pp 47–54

Perry, E (1980)Corkscrews and Bottle Openers, Shire Publications Ltd, Aylesbury, UK

The Design Council (1994) Teaching aids program EDTAP DE9, The Design Council, 28 Haymarket, London SW1Y 4SU, UK

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Steels Cast irons

Al-alloys

Cu-aloys Zn-alloys Ti-alloys

Metals

Elastomers

Aluminas Silicon carbides

Silicon nitrides Zirconias

Ceramics Composites Sandwiches

Segmented structues Lattices Weaves

Hybrids

PE, PP, PET, PC, PS, PEEK

PA (nylons)

Polyesters Phenolics Epoxies

Polymers

Soda glass Borosilicate glass

Silica glass Glass-ceramics

Glasses

Isoprene Neoprene Butyl rubber

Natural rubber Silicones

EVA

Chapter contents

3.2 The families of engineering materials 28

3.3 The definitions of material properties 30

Chapter 3

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Materials, one might say, are the food of design This chapter presents the menu: the full shopping list of materials A successful product — one that performs well, is good value for money and gives pleasure to the user — uses the best materials for the job, and fully exploits their potential and char-acteristics Brings out their flavor, so to speak

The families of materials — metals, polymers, ceramics, and so forth — are introduced in Section 3.2 But it is not, in the end, amaterialthat we seek; it is a certainprofile of properties— the one that best meets the needs of the design The properties, important in thermo-mechanical design, are defined briefly in Section 3.3 It makes boring reading The reader confident in the definitions of moduli, strengths, damping capacities, thermal and electrical conductivities and the like, may wish to skip this, using it for reference, when needed, for the precise meaning and units of the data in the Property Charts that come later Do not, however, skip Sections 3.2 — it sets up the classification structure that is used throughout the book The chapter ends, in the usual way, with a summary

3.2 The families of engineering materials

It is helpful to classify the materials of engineering into the six broad families shown in Figure 3.1: metals, polymers, elastomers, ceramics, glasses, and hybrids The members of a family have certain features in common: similar properties, similar processing routes, and, often, similar applications

Metals have relatively high moduli Most, when pure, are soft and easily deformed They can be made strong by alloying and by mechanical and heat treatment, but they remain ductile, allowing them to be formed by deformation processes Certain high-strength alloys (spring steel, for instance) have ductil-ities as low as percent, but even this is enough to ensure that the material yields before it fractures and that fracture, when it occurs, is of a tough, ductile type Partly because of their ductility, metals are prey to fatigue and of all the classes of material, they are the least resistant to corrosion

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the strength itself depends on the volume of material under load and the time for which it is applied So ceramics are not as easy to design with as metals Despite this, they have attractive features They are stiff, hard, and abrasion-resistant (hence their use for bearings and cutting tools); they retain their strength to high temperatures; and they resist corrosion well

Glasses are non-crystalline (‘‘amorphous’’) solids The commonest are the soda-lime and boro-silicate glasses familiar as bottles and ovenware, but there are many more Metals, too, can be made non-crystalline by cooling them sufficiently quickly The lack of crystal structure suppresses plasticity, so, like ceramics, glasses are hard, brittle and vulnerable to stress concentrations

Polymersare at the other end of the spectrum They have moduli that are low, roughly 50 times less than those of metals, but they can be strong — nearly as strong as metals A consequence of this is that elastic deflections can be large They creep, even at room temperature, meaning that a polymer component under load may, with time, acquire a permanent set And their properties depend on temperature so that a polymer that is tough and flexible at 20C may be brittle at the 4C of a household refrigerator, yet creep rapidly at the 100C of boiling water Few have useful strength above 200C If these aspects are allowed for in the design, the advantages of polymers can be exploited And there are many When combinations of properties, such as strength-per-unit-weight, are important, polymers are as good as metals They are easy to shape: complicated parts performing several functions can be molded from

Steels Cast irons

Al-alloys Cu-alloys Zn-alloys Ti-alloys

Metals

Elastomers

Aluminas Silicon carbides

Silicon nitrides Zirconias

Ceramics Composites

Sandwiches Segmented structues

Lattices and foams

Hybrids

PE, PP, PET, PC, PS, PEEK

PA (nylons) Polyesters Phenolics Epoxies

Polymers

Soda glass Borosilicate glass

Silica glass Glass-ceramics

Glasses

Isoprene Neoprene Butyl rubber Natural rubber

Silicones EVA

Figure 3.1 The menu of engineering materials The basic families of metals, ceramics, glasses, polymers, and elastomers can be combined in various geometries to create hybrids

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a polymer in a single operation The large elastic deflections allow the design of polymer components that snap together, making assembly fast and cheap And by accurately sizing the mold and pre-coloring the polymer, no finishing operations are needed Polymers are corrosion resistant and have low coeffi-cients of friction Good design exploits these properties

Elastomersare long-chain polymers above their glass-transition temperature,

Tg The covalent bonds that link the units of the polymer chain remain intact, but

the weaker Van der Waals and hydrogen bonds that, belowTg, bind the chains to

each other, have melted This gives elastomers unique property profiles: Young’s moduli as low as 103GPa (105time less than that typical of metals) that increase with temperature (all other solids show a decrease), and enormous elastic extension Their properties differ so much from those of other solids that special tests have evolved to characterize them This creates a problem: if we wish to select materials by prescribing a desired attribute profile (as we later in this book), then a prerequisite is a set of attributes common to all materials To overcome this, we settle on a common set for use in the first stage of design, estimating approxi-mate values for anomalies like elastomers Specialized attributes, representative of one family only, are stored separately; they are for use in the later stages

Hybrids are combinations of two or more materials in a pre-determined configuration and scale They combine the attractive properties of the other families of materials while avoiding some of their drawbacks Their design is the subject of Chapters 13 and 14 The family of hybrids includes fiber and particulate composites, sandwich structures, lattice structures, foams, cables, and laminates And almost all the materials of nature — wood, bone, skin, leaf — are hybrids Fiber-reinforced composites are, of course, the most familiar Most of those at present available to the engineer have a polymer matrix reinforced by fibers of glass, carbon or Kevlar (an aramid) They are light, stiff and strong, and they can be tough They, and other hybrids using a polymer as one component, cannot be used above 250C because the polymer softens, but at room temperature their performance can be outstanding Hybrid components are expensive and they are relatively difficult to form and join So despite their attractive properties the designer will use them only when the added performance justifies the added cost Today’s growing emphasis on high performance and fuel efficiency provides increasing drivers for their use

3.3 The definitions of material properties

Each material can be thought of as having a set of attributes: its properties It is not a material,per se, that the designer seeks; it is a specific combination of these attributes: a property-profile The material name is the identifier for a particular property-profile

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Table 3.1 Basic design-limiting material properties and their usual SI units*

Class Property Symbol and units

General Density (kg/m3or Mg/m3)

Price Cm ($/kg)

Mechanical Elastic moduli (Young’s, shear, bulk)

E, G, K (GPa)

Yield strength y (MPa)

Ultimate strength u (MPa)

Compressive strength c (MPa)

Failure strength f (MPa)

Hardness H (Vickers)

Elongation E (–)

Fatigue endurance limit e (MPa)

Fracture toughness K1C (MPa.m1/2)

Toughness G1C (kJ/m2)

Loss coefficient (damping capacity)

(–)

Thermal Melting point Tm (C or K)

Glass temperature Tg (C or K)

Maximum service temperature

Tmax (C or K)

Minimum service temperature

Tmax (C or K)

Thermal conductivity (W/m.K)

Specific heat Cp (J/kg.K)

Thermal expansion coefficient

(K1)

Thermal shock resistance Ts (C or K)

Electrical Electrical resistivity e (.m orm.cm)

Dielectric constant Ed (–)

Breakdown potential Vb (106V/m)

Power factor P (–)

Optical Optical, transparent, translucent, opaque

Yes/No

Refractive index n (–)

Eco-properties Energy/kg to extract material

Ef (MJ/kg)

CO2/kg to extract material

CO2 (kg/kg)

Environmental resistance

Oxidation rates Corrosion rates

Very low, low, average, high, very high

Wear rate constant KA MPa

1

* Conversion factors to imperial and cgs units appear inside the back and front covers of this book

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completeness and precision, they are defined, with their limits, in this section If you think you know how properties are defined, you might jump to Section 3.5, returning to this section only if need arises

General properties

Thedensity(units: kg/m3) is the mass per unit volume We measure it today as Archimedes did: by weighing in air and in a fluid of known density

Theprice, Cm (units: $/kg), of materials spans a wide range Some cost as

little as $0.2/kg, others as much as $1000/kg Prices, of course, fluctuate, and they depend on the quantity you want and on your status as a ‘‘preferred customer’’ or otherwise Despite this uncertainty, it is useful to have an approximate price, useful in the early stages of selection

Mechanical properties

Theelastic modulus(units: GPa or GN/m2) is defined as the slope of the linear-elastic part of the stress–strain curve (Figure 3.2) Young’s modulus, E, describes response to tensile or compressive loading, the shear modulus, G, describes shear loading and the bulk modulus, K, hydrostatic pressure Poisson’s ratio,, is dimensionless: it is the negative of the ratio of the lateral strain,E2, to the axial strain,E1, in axial loading:

¼ "2

"1

In reality, moduli measured as slopes of stress–strain curves are inaccurate, often low by a factor of or more, because of contributions to the strain from

Stress

σ

= F/A

o

Strain ε = δL/L

Slope E = σ/ε 0.2% offset

F Ao

L σy

σu

Metals

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anelasticity, creep and other factors Accurate moduli are measured dynami-cally: by exciting the natural vibrations of a beam or wire, or by measuring the velocity of sound waves in the material

In an isotropic material, the moduli are related in the following ways:

Eẳ 3G

1ỵG=3K; Gẳ E

21ỵị; Kẳ

E

312ị 3:1ị

Commonly1/3 when

G3

8E and KE ð3:2aÞ

Elastomers are exceptional For these1/2 when

G1

3E and KE ð3:2bÞ

Data sources like those described in Chapter 15 list values for all four moduli In this book we examine data forE; approximate values for the others can be derived from equation (3.2) when needed

Thestrengthf, of a solid (units: MPa or MN/m2) requires careful definition

For metals, we identifyfwith the 0.2 percent offset yield strengthy(Figure 3.2),

that is, the stress at which the stress–strain curve for axial loading deviates by a strain of 0.2 percent from the linear-elastic line It is the same in tension and compression For polymers, fis identified as the stress at which the stress–

strain curve becomes markedly non-linear: typically, a strain of percent (Figure 3.3) This may be caused by shear-yielding: the irreversible slipping of molecular chains; or it may be caused by crazing: the formation of low density, crack-like volumes that scatter light, making the polymer look white Polymers

Stress

σ

=

F/A

o

Strain ε = δL/L Brittle: T << Tg

Limited plasticity: T = 0.8 Tg

Cold drawing: T = Tg

Viscous flow: T >> Tg

1% strain

F Ao

L σy

Polymers X

Figure 3.3 Stress–strain curves for a polymer, below, at and above its glass transition temperature,Tg

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are a little stronger (20 percent) in compression than in tension Strength, for ceramics and glasses, depends strongly on the mode of loading (Figure 3.4) In tension, ‘‘strength’’ means the fracture strength,t In compression it means the crushing strengthc, which is much larger; typically

c¼10 to15t ð3:3Þ

When the material is difficult to grip (as is a ceramic), its strength can be measured in bending The modulus of rupture or MoR (units: MPa) is the maximum surface stress in a bent beam at the instant of failure (Figure 3.5)

Stress

σ

= F/A

o

Strain ε = δL/L Slope E = σ/ε

Tension

Compression

F Ao

L σf (compression)

σt (tension)

Ceramics

Figure 3.4 Stress–strain curves for a ceramic in tension and in compression The compressive strengthcis 10 to 15 times greater than the tensile strengtht

F

o

rce F

Deflection δ

Ff Modulus of rupture

σmax= 3FfL = MoR

2bt2 L

b t

Force F Deflection δ

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One might expect this to be the same as the strength measured in tension, but for ceramics it is larger (by a factor of about 1.3) because the volume subjected to this maximum stress is small and the probability of a large flaw lying in it is small also; in simple tension all flaws see the maximum stress

The strength of a composite is best defined by a set deviation from linear-elastic behavior: 0.5 percent is sometimes taken Composites that contain fibers (and this includes natural composites like wood) are a little weaker (up to 30 percent) in compression than tension because fibers buckle In subsequent chapters,ffor composites means the tensile strength

Strength, then, depends on material class and on mode of loading Other modes of loading are possible: shear, for instance Yield under multi-axial loads is related to that in simple tension by a yield function For metals, the Von Mises’ yield function is a good description:

12ị2ỵ 23ị2ỵ 31ị2ẳ2f2 3:4ị

where 1, 2, and are the principal stresses, positive when tensile; 1,

by convention, is the largest or most positive, the smallest or least For

polymers the yield function is modified to include the effect of pressure:

12ị2ỵ 23ị2ỵ 31ị2ẳ2f2 1ỵ

p K

3:5ị

where Kis the bulk modulus of the polymer,2 is a numerical coefficient that characterizes the pressure dependence of the flow strength and the pressure

pis defined by

p¼

31ỵ2ỵ3ị For ceramics, a Coulomb flow law is used:

1B2ẳC 3:6ị

whereBandCare constants

Theultimate (tensile) strength,u(units: MPa), is the nominal stress at which

a round bar of the material, loaded in tension, separates (see Figure 3.2) For brittle solids — ceramics, glasses, and brittle polymers — it is the same as the failure strength in tension For metals, ductile polymers and most composites, it is larger than the strength,f, by a factor of between 1.1 and because of work

hardening or (in the case of composites) load transfer to the reinforcement Cyclic loading not only dissipates energy; it can also cause a crack to nucleate and grow, culminating in fatigue failure For many materials there exists a fatigue orendurance limit,e(units: MPa), illustrated by theNf

curve of Figure 3.6 It is the stress amplitudebelow which fracture does not occur, or occurs only after a very large number (Nf>107) of cycles

The hardness, H, of a material is a crude measure of its strength It is measured by pressing a pointed diamond or hardened steel ball into the surface of the material (Figure 3.7) The hardness is defined as the indenter force

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divided by the projected area of the indent It is related to the quantity we have defined asfby

H3f ð3:7Þ

and this, in the SI system, has units of MPa Hardness is most usually reported in other units, the commonest of which is the VickersHvscale with units of

kg/mm2 It is related toHin the units used here by

Hv¼

H

10

Stress amplitude

∆σ

Cycles to failure, Nf

Endurance limit

σu

∆σe

1

107 cycles

108

∆F Ao

L

Endurance limit

Figure 3.6 The endurance limit,e, is the cyclic stress that causes failure inNf¼107cycles

Load

P

Projected area A

H = P/A

Load P

Projected area A

Hardness

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Thetoughness, G1C, (units: kJ/m2), and the fracture toughness, K1C, (units: MPa.m1/2or MN/m1/2), measure the resistance of a material to the propagation of a crack The fracture toughness is measured by loading a sample containing a deliberately-introduced crack of length 2c (Figure 3.8), recording the tensile stress cat which the crack propagates The quantity K1Cis then calculated from

K1CẳYc c

p

3:8ị

and the toughness from

G1Cẳ

K2 1C

E1ỵvị 3:9ị

whereYis a geometric factor, near unity, that depends on details of the sample geometry,Eis Young’s modulus andis Poisson’s ratio Measured in this way

K1CandG1Chave well-defined values for brittle materials (ceramics, glasses, and many polymers) In ductile materials a plastic zone develops at the crack tip, introducing new features into the way in which cracks propagate that necessitate more involved characterization Values for K1C and G1C are, nonetheless, cited, and are useful as a way of ranking materials

The loss-coefficient, (a dimensionless quantity), measures the degree to which a material dissipates vibrational energy (Figure 3.9) If a material is loaded elastically to a stress,max, it stores an elastic energy

U¼ Zmax

0

d"1

2 2max

E

K1C=σc(πa)1/2

Stress

σ

= F/A

o

Strain ε = δL/L

σc

Fracture toughness

2c

Figure 3.8 The fracture toughness,KIC, measures the resistance to the propagation of a crack The failure strength of a brittle solid containing a crack of length 2cisKICẳYc= c

p ị

whereYis a constant near unity

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per unit volume If it is loaded and then unloaded, it dissipates an energy U¼

I

d" The loss coefficient is

ẳ U

2U 3:10ị

The value of usually depends on the time-scale or frequency of cycling Other measures of damping include thespecific damping capacity, D¼U/U, thelog decrement, (the log of the ratio of successive amplitudes of natural vibrations), thephase-lag, , between stress and strain, and the ‘‘Q’’-factor or

resonance factor, Q When damping is small ( <0.01) these measures are related by

¼ D

2ẳ

ẳtan ẳ

1

Q 3:11ị

but when damping is large, they are no longer equivalent Thermal properties

Two temperatures, the melting temperature, Tm, and the glass temperature,

Tg(units for both: K or C) are fundamental because they relate directly to the

strength of the bonds in the solid Crystalline solids have a sharp melting point,Tm Non-crystalline solids not; the temperatureTgcharacterizes the

transition from true solid to very viscous liquid It is helpful, in engineering

S

tress

σ

=

F

/A

o

Strain ε = δL/L Loss coefficient

Area

U

Area

∆UU

∆U η =

2πU ∆F

Ao

L

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design, to define two further temperatures: themaximumandminimum service temperatures TmaxandTmin(both: K or C) The first tells us the highest

tem-perature at which the material can reasonably be used without oxidation, chemical change, or excessive creep becoming a problem The second is the temperature below which the material becomes brittle or otherwise unsafe to use

The rate at which heat is conducted through a solid at steady state (meaning that the temperature profile does not change with time) is measured by the

thermal conductivity,(units: W/m.K) Figure 3.10 shows how it is measured: by recording the heat flux q (W/m2) flowing through the material from a surface at higher temperatureT1to a lower one atT2separated by a distanceX

The conductivity is calculated from Fourier’s law:

q¼ dT dX¼

ðT1T2Þ

X ð3:12Þ

The measurement is not, in practice, easy (particularly for materials with low conductivities), but reliable data are now generally available

When heat flow is transient, the flux depends instead on thethermal diffu-sivity,a(units: m2/s), defined by

aẳ

Cp

3:13ị

where is the density andCp is thespecific heat at constant pressure (units:

J/kg.K) The thermal diffusivity can be measured directly by measuring the decay of a temperature pulse when a heat source, applied to the material, is switched off; or it can be calculated from, via equation (3.13) This requires

H

eat

flux

q

Temperature gradient (T1TT – T2TT )/X Slope λ

Insulation Sample Heat

input

q W/m

q 22

Heat sink

q W/m

q

T1 T

T TTT2

X

∆T q= q − λ

∆X

Thermal conductivity

Figure 3.10 The thermal conductivitymeasures the flux of heat driven by a temperature gradient dT/dX

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values forCp It is measured by the technique of calorimetry, which is also the

standard way of measuring the glass temperatureTg

Most materials expand when they are heated (Figure 3.11) The thermal strain per degree of temperature change is measured by the linear thermal-expansion coefficient,(units: K1or, more conveniently, as ‘‘microstrain/C’’

or 106C1) If the material is thermally isotropic, the volume expansion, per

degree, is If it is anisotropic, two or more coefficients are required, and the volume expansion becomes the sum of the principal thermal strains

The thermal shock resistance Ts (units: K or C) is the maximum

tem-perature difference through which a material can be quenched suddenly without damage It, and the creep resistance, are important in high-temperature design Creep is the slow, time-dependent deformation that occurs when materials are loaded above about1

3Tmor23Tg Design against creep is a specialized subject Here we rely instead on avoiding the use of a material above its maximum service temperature, Tmax, or, for polymers, its ‘‘heat

deflection temperature’’

Electrical properties

Theelectrical resistivity,e(SI units.m, but commonly reported in units of m.cm) is the resistance of a unit cube with unit potential difference between a pair of it faces It is measured in the way shown in Figure 3.12 It has an immense range, from a little more than 108in units of.m (equal to 1m.cm) for good conductors to more than 1016.m (1024m.cm) for the best insula-tors The electrical conductivity is simply the reciprocal of the resisitivity

Temperature change ∆T

Slope α

Ther

mal str

ain

ε

=

δ

L/L

Heater Sample

∆L L

α α = ∆L

∆T L

Thermal expansion

Insulation

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When an insulator is placed in an electric field, it becomes polarized and charges appear on its surfaces that tend to screen the interior from the electric field The tendency to polarize is measured by the dielectric constant, Ed

(a dimensionless quantity) Its value for free space and, for practical purposes, for most gasses, is Most insulators have values between and 30, though low-density foams approach the value because they are largely air

Thebreakdown potential(units: MV/m) is the electrical potential gradient at which an insulator breaks down and a damaging surge of current flows through it It is measured by increasing, at a uniform rate, a 60 Hz alternating potential applied across the faces of a plate of the material until breakdown occurs

Polarization in an electric field involves the motion of charge particles (electrons, ions, or molecules that carry a dipole moment) In an oscillating field, the charged particles are driven between two alternative configurations This charge-motion corresponds to an electric current that — if there were no losses — would be 90 out of phase with the voltage In real dielectrics, the motion of the charged particles dissipates energy and the current leads the voltage by something less that 90; the loss angleis the deviation The loss tangent is the tangent of this angle Thepower factor(dimensionless) is the sine of the loss angle, and measures the fraction of the energy stored in the dielectric at peak voltage that is dissipated in a cycle; when small, it is equal to the loss tangent Theloss factoris the loss tangent times the dielectric constant

Optical properties

All materials allow some passage of light, although for metals it is exceed-ingly small The speed of light when in the material, v, is always less

P

otential diff

erence

∆

V

Current ι

Resistance

R = ∆V/ι Electrical resistivity

ι ι

Area A

∆V

X

Resistivity

ρe = A

ι ∆V

X

Figure 3.12 Electrical resistivity is measured as the potential gradientV/Xdivided by the current density,i/A

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than that in vacuum, c A consequence is that a beam of light striking the surface of such a material at an angle , the angle of incidence, enters the material at an angle , the angle of refraction The refractive index, n

(dimensionless), is

n¼c

¼

sin

sin ð3:14Þ

It is related to the dielectric constant,Ed, by

n ffiffiffiffiffi"d

p

It depends on wavelength The denser the material, and the higher its dielectric constant, the larger is the refractive index When n¼1, the entire incident intensity enters the material, but whenn>1, some is reflected If the surface is smooth and polished, it is reflected as a beam; if rough, it is scattered The percentage reflected,R, is related to the refractive index by

Rẳ n1

nỵ1

100 ð3:15Þ

Asnincreases, the value ofRtends to 100 percent

Eco properties

The contained or production energy (units MJ/kg) is the energy required to extract kg of a material from its ores and feedstocks The associated CO2

production (units: kg/kg) is the mass of carbon dioxide released into the atmosphere during the production of kg of material These and other eco-attributes are the subject of Chapter 16

Environmental resistance

Some material attributes are difficult to quantify, particularly those that involve the interaction of the material within the environments in which it must operate Environmental resistance is conventionally characterized on a discrete 5-point scale: very good, good, average, poor, very poor ‘‘Very good’’ means that the material is highly resistant to the environment, ‘‘very poor’’ that it is completely non-resistant or unstable The categorization is designed to help with initial screening; supporting information should always be sought if environmental attack is a concern Ways of doing this are described later

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The wear resistance of the surface is characterized by the Archard wear con-stant, KA(units: MPa1), defined by the equation

W

A ẳKAP 3:16ị

where A is the area of the surface and P the normal force pressing them together Approximate data for KA appear in Chapter 4, but must be

inter-preted as the property of the sliding couple, not of just one member of it

There are six important families of materials for mechanical design: metals, ceramics, glasses, polymers, elastomers, and hybrids that combine the prop-erties of two or more of the others Within a family there is certain common ground: ceramics as a family are hard, brittle, and corrosion resistant; metals are ductile, tough, and good thermal and electrical conductors; polymers are light, easily shaped, and electrical insulators, and so on — that is what makes the classification useful But in design we wish to escape from the constraints of family, and think, instead, of the material name as an identifier for a certain property-profile — one that will, in later chapters, be compared with an ‘‘ideal’’ profile suggested by the design, guiding our choice To that end, the properties important in thermo-mechanical design were defined in this chapter In Chapter we develop a way of displaying these properties so as to maximize the freedom of choice

W

e

ar v

olume

V

Sliding distance S

W = V/S

Sliding velocity v

Load P

Area A P1 P2

P3

Wear rate

Figure 3.13 Wear is the loss of material from surfaces when they slide The wear resistance is measured by the Archard wear constantKA

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3.5 Further reading

Definitions of material properties can be found in numerous general texts on engi-neering materials, among them those listed here

Ashby, M.F and Jones, D.R.H (1996)Engineering Materials 1, and Introduction to their Properties and Applications, 2nd edition, Pergamon Press, Oxford, U.K ISBN 0–7506–3081–7

ASM Engineered Materials Handbook (2004) ‘‘Testing and characterisation of poly-meric materials’’, ASM International, Metals Park, OH, USA (An on-line, sub-scription-based resource, detailing testing procedures for polymers.)

ASM Handbooks, Volume (2004) ‘‘Mechanical testing and evaluation’’ ASM Inter-national, Metals Park, Ohio, USA (An on-line, subscription-based resource, detailing testing procedures for metals and ceramics.)

ASTM Standards (1988) Vol 08.01 and 08.02 Plastics; (1989) Vol 04.02 Concrete; (1990) Vols 01.01 to 01.05 Steels; Vol 0201 Copper alloys; Vol 02.03 Aluminum alloys; Vol 02.04 Non-ferrous alloys; Vol 02.05 Coatings; Vol 03.01 Metals at high and low temperatures; Vol 04.09 Wood; Vols 09.01 and 09.02 Rubber, American Society for Testing Materials, 1916 Race Street, Philadelphia, PA, USA ISBN 0–8031–1581–4 (The ASTM set standards for materials testing.)

Callister, W.D (2003) Materials Science and Engineering, an Introduction, 6th edition, John Wiley, New York, USA ISBN 0–471–13576–3 (A well-respected materials text, now in its 6th edition, widely used for materials teaching in North America.)

Charles, J.A., Crane, F.A.A and Furness, J.A.G (1997)Selection and Use of Engineering Materials, 3rd edition, Butterworth-Heinemann, Oxford, UK ISBN 0–7506–3277–1 (A materials-science approach to the selection of materials.)

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Chapter contents

4.1 Introduction and synopsis 46 4.2 Exploring material properties 46 4.3 The material property charts 50 4.4 Summary and conclusions 77

Chapter 4

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Material properties limit performance We need a way of surveying them, to get a feel for the values design-limiting properties can have One property can be displayed as a ranked list or bar-chart But it is seldom that the performance of a component depends on just one property Almost always it is a combi-nation of properties that matter: one thinks, for instance, of the strength-to-weight ratio,f/, or the stiffness-to-weight ratio,E/, that enter light-weight design This suggests the idea of plotting one property against another, map-ping out the fields in property-space occupied by each material class, and the sub-fields occupied by individual materials

The resulting charts are helpful in many ways They condense a large body of information into a compact but accessible form; they reveal correlations between material properties that aid in checking and estimating data; and in later chapters they become tools for tackling real design problems

The idea of a materials-selection chart is described briefly in Section 4.2 Section 4.3 is not so brief: it introduces the charts themselves There is no need to read it all, but it is helpful to persist far enough to be able to read and interpret the charts fluently, and to understand the meaning of the design guidelines that appear on them If, later, you use one chart, you should read the background to it, given here, to be sure of interpreting it correctly

As explained in the preface, you may copy and distribute these charts without infringing copyright.1

4.2 Exploring material properties

The properties of engineering materials have a characteristic span of values The span can be large: many properties have values that range over five or more decades One way of displaying this is as a bar-chart like that of Figure 4.1 for thermal conductivity Each bar represents a single material The length of the bar shows the range of conductivity exhibited by that material in its various forms The materials are segregated by class Each class shows a characteristic range: metals, have high conductivities; polymers have low; ceramics have a wide range, from low to high

Much more information is displayed by an alternative way of plotting properties, illustrated in the schematic of Figure 4.2 Here, one property (the modulus,E, in this case) is plotted against another (the density, ) on loga-rithmic scales The range of the axes is chosen to include all materials, from the

1

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lightest, flimsiest foams to the stiffest, heaviest metals It is then found that data for a given family of materials (e.g polymers) cluster together on the chart; the sub-range associated with one material family is, in all cases, much smaller than the fullrange of that property Data for one family can be enclosed in a property-envelope, as Figure 4.2 shows Within it lie bubbles enclosing classes and sub-classes

All this is simple enough — just a helpful way of plotting data But by choosing the axes and scales appropriately, more can be added The speed of sound in a solid depends on E and ; the longitudinal wave speed v, for instance, is

v¼ E

1=2

or (taking logs)

logEẳlogỵ2logv

For a fixed value of v, this equation plots as a straight line of slope on Figure 4.2 This allows us to add contours of constant wave velocity to the chart: they are the family of parallel diagonal lines, linking materials in which longitudinal waves travel with the same speed All the charts allow additional fundamental relationships of this sort to be displayed And there is more: design-optimizing parameters called material indicesalso plot as contours on to the charts But that comes in Chapter

Metals

T

h

er

m

a

l c

onduc

ti

v

it

y

(

W

/m

.K

)

0.01 0.1 10

1 100 1000

Ceramics

and glasses Polymers and elastomers

Lead alloys Carbon steels

Ti alloys Mg alloys Al alloys Cu alloys

PA

PMMA

Butyl rubber Silicone

elastomers Concrete

Al2O3

SiC

Si3N4

Thermal conductivity B4C

Epoxies PVC

MFA 04

Stainless steels

Glass Brick AlN

PP ABS

Figure 4.1 A bar-chart showing thermal conductivity for families of solid Each bar shows the range

of conductivity offered by a material, some of which are labeled

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Among the mechanical and thermal properties, there are 30 or so that are of primary importance, both in characterizing the material, and in engineering design They were listed in Table 3.1: they include density, moduli, strength, hardness, toughness, thermal and electrical conductivities, expansion coeffi-cient, and specific heat The charts display data for these properties for the families and classes of materials listed in Table 4.1 The list is expanded from the original six of Figure 3.1 by distinguishing composites from foams and from woods though all are hybrids and by distinguishing the high-strength engineering ceramics (like silicon carbide) from the low strength, porous ceramics(like brick) Within each family, data are plotted for a representative set of materials, chosen both to span the full range of behavior for the class, and to include the most common and most widely used members of it In this way the envelope for a family encloses data not only for the materials listed in Table 4.1, but virtually all other members of the family as well

Longitudinal wave speed

1033 m/s

1000 m/s22 3 x103m/s

3 x1000 m/s22

Metals

Elastomers Ceramics

Woods

Foams

0.1 10

1 100

0.01 1000

100

0.1 10

Density (Mg/m3)

Yo

u

n

g

’s

mo

d

u

lu

s

,

E

(GPa)

E

Modulus-Density

MFA, 04

Polymers

Compposites

Figure 4.2 The idea of a materials property chart: Young’s modulus,E, is plotted against the density,

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Table 4.1 Material families and classes

Family Classes Short name

Metals Aluminum alloys Al alloys

(the metals and alloys Copper alloys Cu alloys

of engineering) Lead alloys Lead alloys

Magnesium alloys Mg alloys

Nickel alloys Ni alloys

Carbon steels Steels

Stainless steels Stainless steels

Tin alloys Tin alloys

Titanium alloys Ti alloys

Tungsten alloys W alloys

Lead alloys Pb alloys

Zinc alloys Zn alloys

Ceramics Alumina Al2O3

Technical ceramics Aluminum nitride AlN

(fine ceramics capable Boron carbide B4C

of load-bearing application) Silicon Carbide SiC

Silicon Nitride Si3N4

Tungsten carbide WC

Non-technical ceramics Brick Brick

(porous ceramics of Concrete Concrete

construction) Stone Stone

Glasses Soda-lime glass Soda-lime glass

Borosilicate glass Borosilicate glass

Silica glass Silica glass

Glass ceramic Glass ceramic

Polymers Acrylonitrile butadiene styrene ABS

(the thermoplastics and Cellulose polymers CA

thermosets of engineering) Ionomers Ionomers

Epoxies Epoxy

Phenolics Phenolics

Polyamides (nylons) PA

Polycarbonate PC

Polyesters Polyester

Polyetheretherkeytone PEEK

Polyethylene PE

Polyethylene terephalate PET or PETE

Polymethylmethacrylate PMMA

Polyoxymethylene (Acetal) POM

Polypropylene PP

Polystyrene PS

Polytetrafluorethylene PTFE

Polyvinylchloride PVC

(62)

The charts that follow show a range of values for each property of each material Sometimes the range is narrow: the modulus of copper, for instance, varies by only a few percent about its mean value, influenced by purity, texture and such like Sometimes it is wide: the strength of alumina-ceramic can vary by a factor of 100 or more, influenced by porosity, grain size, and composition Heat treatment and mechanical working have a profound effect on yield strength and toughness of metals Crystallinity and degree of cross-linking greatly influence the modulus of polymers Thesestructure-sensitiveproperties appear as elongated bubbles within the envelopes on the charts A bubble encloses a typical range for the value of the property for a single material class Envelopes (heavier lines) enclose the bubbles for a family

The data plotted on the charts have been assembled from a variety of sources, documented in Chapter 15

4.3 The material property charts

The Modulus–Density chart

Modulus and density are familiar properties Steel is stiff, rubber is compliant: these are effects of modulus Lead is heavy; cork is buoyant: these are effects of density Figure 4.3 shows the full range of Young’s modulus,E, and density,, for engineering materials Data for members of a particular family of material cluster together and can be enclosed by an envelope (heavy line) The same

Table 4.1 (Continued)

Family Classes Short name

Elastomers Butyl rubber Butyl rubber

(engineering rubbers, EVA EVA

natural and synthetic) Isoprene Isoprene

Natural rubber Natural rubber

Polychloroprene (Neoprene) Neoprene

Polyurethane PU

Silicone elastomers Silicones

Hybrids Carbon-fiber reinforced polymers CFRP

Composites Glass-fiber reinforced polymers GFRP

SiC reinforced aluminum Al-SiC

Foams Flexible polymer foams Flexible foams

Rigid polymer foams Rigid foams

Natural materials Cork Cork

Bamboo Bamboo

(63)

family-envelopes appear on all the diagrams: they correspond to the main headings in Table 4.1

The density of a solid depends on three factors: the atomic weight of its atoms or ions, their size, and the way they are packed The size of atoms does not vary much: most have a volume within a factor of two of 21029m3 Packing fractions not vary much either — a factor of two, more or less: close-packing gives a packing fraction of 0.74; open networks (like that of the diamond-cubic structure) give about 0.34 The spread of density comes mainly from that of atomic weight, ranging from for hydrogen to 238 for uranium Metals are dense because they are made of heavy atoms, packed densely; polymers have low densities because they are largely made of carbon (atomic weight: 12) and hydrogen (atomic weight: 1) in low-density amorphous or crystalline packings Ceramics, for the most part, have lower densities than

E1/3 ρ E1/2 ρ E ρ

104m/s

103m/s

102 m/s Longitudinal wave speed Guidelines for minimum mass design D

Deennsisitty,y,ρρ ((MMgg//mm3)

0 0011

YY oo uu nn gg ''sm o s mo dd uu lluu ss, EE ((G P a )

10-44

0.1 10

10-3 10-2 10-1 10 100 1000 Polyesterolyest P y Foams Polymers and elastomersy Metals Technical ceramics Composites

Natural materialsaturaa

Lead alloys W alloyslloys Steels Ti alloys Mg alloys M o CFRP C GFRP Al alloys A mer mer Rigid polym foams Flexible polymer foams

Ni alloysalloys

Cu alloysy

Zinc alloysalloys PA PEEK PMMA PC PETT Cork Wood Butyl rubber Silicone elastomers Concretee WC WC Al2O3

SiC Si Si33NN44 Young's modulus - Density

B4C

Epoxies PS PTFE EVA Neoprene Isoprene Polyurethane Leatherher L L MFA, 04 PP PE PE

Glassassss Glass

n // grainn // graig

ain a a a graaa g g g T

Figure 4.3 Young’s modulus,E, plotted against density, The heavy envelopes enclose data for a

given class of material The diagonal contours show the longitudinal wave velocity The guidelines of constantE/,E1/2/andE1/3/allow selection of materials for minimum weight, deflection-limited, design

(64)

metals because they contain light O, N or C atoms Even the lightest atoms, packed in the most open way, give solids with a density of around Mg/m3. Materials with lower densities than this are foams — materials made up of cells containing a large fraction of pore space

Themoduliof most materials depend on two factors: bond stiffness, and the density of bonds per unit volume A bond is like a spring: it has a spring constant,S(units: N/m) Young’s modulus,E, is roughly

E¼ S r0

ð4:1Þ wherer0is the ‘‘atom size’’ (r30is the mean atomic or ionic volume) The wide

range of moduli is largely caused by the range of values ofS The covalent bond is stiff (S¼20–200 N/m); the metallic and the ionic a little less so (S¼15– 100 N/m) Diamond has a very high modulus because the carbon atom is small (giving a high bond density) and its atoms are linked by very strong springs (S¼200 N/m) Metals have high moduli because close-packing gives a high bond density and the bonds are strong, though not as strong as those of dia-mond Polymers contain both strong diamond-like covalent bonds and weak hydrogen or Van-der-Waals bonds (S¼0.5–2 N/m); it is the weak bonds that stretch when the polymer is deformed, giving low moduli

But even large atoms (r0¼31010m) bonded with the weakest bonds (S¼0.5 N/m) have a modulus of roughly

E¼ 0:5

310101 Gpa ð4:2Þ

This is the lower limit for true solids The chart shows that many materials have moduli that are lower than this: they are either elastomers or foams Elastomers have a lowEbecause the weak secondary bonds have melted (their glass temperature,Tg, is below room temperature) leaving only the very weak ‘‘entropic’’ restoring force associated with tangled, long-chain molecules; and foams have low moduli because the cell walls bend easily (allowing large displacements) when the material is loaded

The chart shows that the modulus of engineering materials spans decades,2 from 0.0001 GPa (low-density foams) to 1000 GPa (diamond); the density spans a factor of 2000, from less than 0.01 to 20 Mg/m3 Ceramics as a family are very stiff, metals a little less so — but none have a modulus less than 10 GPa Polymers, by contrast, all cluster between 0.8 and GPa To have a lower modulus than this the material must be either an elastomer or a foam At the level of approximation of interest here (that required to reveal the relationship between the properties of materials classes) we may approximate

2 Very low density foams and gels (which can be thought of as molecular-scale, fluid-filled, foams) can

have lower moduli than this As an example, gelatin (as in Jello) has a modulus of about 105GPa Their

(65)

the shear modulus,G, by3E/8 and the bulk modulus,K, byE, for all materials except elastomers (for whichG¼E/3 andKE) allowing the chart to be used for these also

The log-scales allow more information to be displayed As explained in the last section, the velocity of elastic waves in a material, and the natural vibration frequencies of a component made of it, are proportional to (E/)1/2 Contours of this quantity are plotted on the chart, labeled with the longitudinal wave speed It varies from less than 50 m/s (soft elastomers) to a little more than 104m/s (stiff ceramics) We note that aluminum and glass, because of their low densities, transmit waves quickly despite their low moduli One might have expected the wave velocity in foams to be low because of the low modulus, but the low density almost compensates That in wood, across the grain, is low; but along the grain, it is high — roughly the same as steel — a fact made use of in the design of musical instruments

The chart helps in the common problem of material selection for applica-tions in which mass must be minimized Guidelines corresponding to three common geometries of loading are drawn on the diagram They are used in the way described in Chapters and to select materials for elastic design at minimum weight

The strength–density chart

The modulus of a solid is a well-defined quantity with a sharp value The strength is not It is shown, plotted against density,, in Figure 4.4

The word ‘‘strength’’ needs definition (see also Chapter 3, Section 3.3) For metals and polymers, it is the yield strength, but since the range of materials includes those that have been worked or hardened in some other way as well as those that have been annealed, the range is large For brittle ceramics, the strength plotted here is the modulus of rupture:the strength in bending It is slightly greater than the tensile strength, but much less than the compression strength, which, for ceramics is 10 to 15 times larger For elastomers, strength means the tensiletear-strength For composites, it is thetensile failure strength (the compressive strength can be less by up to 30 percent because of fiber buckling) We will use the symbolffor all of these, despite the different failure mechanisms involved to allow a first-order comparison

The considerable vertical extension of the strength-bubble for an individual material class reflects its wide range, caused by degree-of-alloying, work hardening, grain size, porosity and so forth As before, members of a family cluster together and can be enclosed in an envelope, each of which occupies a characteristic area of the chart

(66)

wide range is that of thelattice resistanceorPeierls stress: the intrinsic resistance of the structure to plastic shear Plastic shear in a crystal involves the motion of dislocations Pure metals are soft because the non-localized metallic bond does little to prevent dislocation motion, whereas ceramics are hard because their more localized covalent and ionic bonds (which must be broken and reformed when the structure is sheared), lock the dislocations in place In non-crystalline solids we think instead of the energy associated with the unit step of the flow process: the relative slippage of two segments of a polymer chain, or the shear of a small molecular cluster in a glass network Their strength has the same origin as that underlying the lattice resistance: if the unit step involves breaking strong bonds (as in an inorganic glass), the materials will be strong; if it only involves the rupture of weak bonds (e.g the Van-der-Waals bonds in polymers), it will be weak Materials that fail by fracture so because the lattice resistance or its amorphous equivalent is so large that atomic separation (fracture) happens first

D

Densiitty, ρ ((MMg//m3)

0 0.0011

Strength, trength , σσf ((MM PP aa ))

0.0011

10

0.1 11

0.1 10 100 1000 10000 Foams Polymers and elastomers Metals Ceramics Composites NaturalN materials Lead alloys Tungsten alloysalloys Steelss Ti alloys

Mg alloyso CFRPF

GFRPF Al alloys

Rigid polymer Rigid pol mer

foams Flexible polymer foams Ni alloys Copperpp alloys Zinc alloys PA PEEKE PMMA

PC PETT

Cork Wood Butyl rubberr Silicone elastomers Concrete Tungsten carbide Al2O3

SiC Si3N4 Strength - Density

MFA, 04

fo e po oys σf 1/2 f ρ σf 2/3 f ρ σff ρ Guidelines for minimum mass design Metals and polymers: yield strength

Ceramics and glasses: MOR Elastomers: tensile tear strength Composites: tensile failure

Figure 4.4 Strength,f, plotted against density,(yield strength for metals and polymers,

compressive strength for ceramics, tear strength for elastomers and tensile strength for composites) The guidelines of constantf/,2

=3 f =and

1=2

(67)

When the lattice resistance is low, the material can be strengthened by introducing obstacles to slip In metals this is achieved by adding alloying ele-ments, particles, grain boundaries, and other dislocations (‘‘work hardening’’); and in polymers by cross-linking or by orienting the chains so that strong covalent as well as weak Van-der-Waals bonds must be broken when the material deforms When, on the other hand, the lattice resistance is high, further hardening is superfluous — the problem becomes that of suppressing fracture

An important use of the chart is in materials selection in light-weight plastic design Guidelines are shown for materials selection in the minimum-weight design of ties, columns, beams and plates, and for yield-limited design of moving components in which inertial forces are important Their use is described in Chapters and

The modulus–strength chart

High tensile steel makes good springs But so does rubber How is it that two such different materials are both suited for the same task? This and other questions are answered by Figure 4.5, one of the most useful of all the charts It shows Young’s modulus,E, plotted against strength,f The qualifications on ‘‘strength’’ are the same as before: it means yield strength for metals and polymers, modulus of rupture for ceramics, tear strength for elastomers, and tensile strength for composite and woods; the symbol fis used for them all Contours ofyield strain,f/E(meaning the strain at which the material ceases to be linearly elastic), appear as a family of straight parallel lines

Examine these first Engineering polymers have large yield strains of between 0.01 and 0.1; the values for metals are at least a factor of 10 smaller Com-posites and woods lie on the 0.01 contour, as good as the best metals Elas-tomers, because of their exceptionally low moduli, have values of f/Elarger than any other class of material: typically to 10

The distance over which inter-atomic forces act is small — a bond is broken if it is stretched to more than about 10 percent of its original length So the force needed to break a bond is roughly

FSr0

10 ð4:3Þ

whereS, as before, is the bond stiffness If shear breaks bonds, the strength of a solid should be roughly

f

F r2

¼ S

10r0

¼ E 10 or

f

E

1

10 ð4:4Þ

(68)

The chart shows that, for some polymers, the failure strain approaches this value For most solids it is less, for two reasons

First, non-localized bonds (those in which the cohesive energy derives from the interaction of one atom with large number of others, not just with its nearest neighbors) are not broken when the structure is sheared The metallic bond, and the ionic bond for certain directions of shear, are like this; very pure metals, for example, yield at stresses as low as E/10,000, and strengthening mechanisms are needed to make them useful in engineering The covalent bond islocalized; and covalent solids do, for this reason, have yield strength that, at low temperatures, are as high asE/10 It is hard to measure them (though it can sometimes be done by indentation) because of the second reason for weakness: they generally contain defects — concentrators of stress — from which shear or

Strength,

Strength σσf f((MMPPaa)

YY o u n g 's m o d u lu s, E (G PP a )

0 11 1010 100 1000

0.01 0.1 10 100 1000

= 10-4 Yield strain Y

σf E

10-3

10-2 0

1000-1-1-1-1 Non-technical ceramics MFA, 04 Foams Polymers Metals Technical ceramics Composites

Lead alloysead y

W alloys W

Ti alloys

Mg alloysy CFRP

GFRP

Al alloyso

Rigid polymer foams Ni alloys Cu alloys Cu a Zinc alloys Z PMMAA Cork Wood W Woo Polyurethane Silicone Sl

elastomersa Concreter

Al22O3

SiC AlN

Modulus - Strength

B4C

EVA Leather

Cast irons WCC

Soda glassoda Silica glassilica

Silicon S

Stone Brickk

Epoxies

Ionomers

Steelss

Polyurethaneoolyu

PA PCC PE PTFE PS P PP P Phenolich Metals and polymers: yield strength

Ceramics and glasses: MoR Elastomers: tensile tear strength Composites: tensile failure

ne

σf2 E

σfff E σf3/222

E Design guide lines Buckling before yield Yield before buckling Elastomers

Figure 4.5 Young’s modulus,E, plotted against strength,f The design guidelines help with the

(69)

fracture can propagate, at stresses well below the ‘‘ideal’’E/10 Elastomers are anomalous (they have strengths of about E) because the modulus does not derive from bond-stretching, but from the change in entropy of the tangled molecular chains when the material is deformed

Materials with high strength and low modulus lie towards the bottom right Such materials tend to buckle before they yield when loaded as panels or columns Those near the top left have high modulus and low strength: they end toyield before buckling

This has not yet explained how to choose good materials to make springs This involves the design guidelines shown on the chart The way to use them is described in Chapter 6, Section 6.7

The specific stiffness–specific strength chart

Many designs, particularly those for things that move, call for stiffness and strength at minimum weight To help with this, the data of the previous chart are replotted in Figure 4.6 after dividing, for each material, by the density; it showsE/plotted againstf/

Composites, particularly CFRP, emerge as the material class with the most attractive specific properties, one of the reasons for their increasing use in aerospace Ceramics have exceptionally high stiffness per unit weight, and the strength per unit weight is as good as metals Metals are penalized because of their relatively high densities Polymers, because their densities are low, better on this chart than on the last one

The chart has application in selecting materials for light springs and energy-storage devices But that too has to wait till Section 6.7

The fracture toughness–modulus chart

Increasing the strength of a material is useful only as long as it remains plastic and does not fail by fast fracture The resistance to the propagation of a crack is measured by the fracture toughness,K1C It is plotted against modulus E in Figure 4.7 The range is large: from less than 0.01 to over 100 MPa.m1/2 At the lower end of this range are brittle materials, which, when loaded, remain elastic until they fracture For these, linear-elastic fracture mechanics works well, and the fracture toughness itself is a well-defined property At the upper end lie the super-tough materials, all of which show substantial plasticity before they break For these the values ofK1Care approximate, derived from critical J-integral (Jc) and critical crack-opening displacement ( c) measure-ments (by writingK1C¼(EJc)1/2, for instance) They are helpful in providing a ranking of materials The figure shows one reason for the dominance of metals in engineering; they almost all have values ofK1Cabove 20 MPa.m1/2, a value often quoted as a minimum for conventional design

(70)

As a general rule, the fracture toughness of polymers is less than that of ceramics Yet polymers are widely used in engineering structures; ceramics, because they are ‘‘brittle’’, are treated with much more caution Figure 4.7 helps resolve this apparent contradiction Consider first the question of the necessary condition for fracture It is that sufficient external work be done, or elastic energy released, to supply the surface energy,per unit area, of the two new surfaces that are created We write this as

G2 ð4:5Þ

where G is the energy release-rate Using the standard relation K¼(EG)1/2 betweenGand stress intensityK, we find

K ð2EÞ1=2 ð4:6Þ

Specific strength, σf/ρ(MPa/(kg/m3))

S p e c if ic m oo dd uu lluu sE / s , E/ ρρ (GPa/(kg/m (GPa 3)) 10

10 10-3 10-2 10

10-5555

10-4444

0 -3333

0 -2222

10-1

1

= 10-4 Yield strain σf E 10-3 10-2 N Non-technical ceramics Foams Polymers Metals Technical ceramics Composites Lead alloys

Ti alloysMg alloys CFRP C

GFRP

Al alloyss A A A Rigid polymer Rigid polymer foams

Cu alloysl C

Zinc alloysc

PMMAA Wood

Polyurethanee

Silicones e Concrete

Al2O3

SiCC AlN

Specific modulus - Specific strength

B4C

EVA Leather

Cast irons Cast irons WCC

Soda glassd Silica glassl

Silicon Stone Brick Epoxiesox Epoxiespoxi Ionomers Steels PA PC P PE PTFE PS P PP

Si3NN44

Cork

MFA, 04

Metals and polymers: yield strength Ceramics and glasses: MoR Elastomers: tensile tear strength Composites: tensile failure

Po a

σf2 E

σff E σ

f3/222 E Design guide lines Buckling before yield Yield before buckling Elastomers

Figure 4.6 Specific modulus,E/plotted against specific strengthf/ The design guidelines help with

(71)

Now the surface energies, , of solid materials scale as their moduli; to an adequate approximationEr0/20 wherer0is the atom size, giving

KE r0 20

1=2

ð4:7Þ We identify the right-hand side of this equation with a lower-limiting value of K1C, when, taking as 21010m,

K1Cịmin

E ẳ

r0

20

1=2

3106m1=2 ð4:8Þ

This criterion is plotted on the chart as a shaded, diagonal band near the lower right corner It defines alower limitforK1C The fracture toughness cannot be less than this unless some other source of energy such as a chemical reaction,

100

10

1

0.1

0.01

Young's modulus, E (GPa)

F ract u re toughness, K1 C (MP a m 1/ 2)

0.001 0.01 0.1 10 100 1000

0.01 0.1 10 100 1000 Foams Polymers and elastomers Metals Technical ceramics Composites Natural materials Lead alloys W alloys Steels Ti alloys Mg alloys CFRP GFRP Al alloys Rigid polymer foams Flexible polymer foams Ni alloys Cu alloys Zinc alloys PS PTFE PC Cork Wood Butyl rubber Silicone elastomers Concrete

Al2O3

SiC Si3N4 Fracture toughness - Modulus

B4C

PP EVA Polyurethane Leather Non-technical ceramics Cast irons WC Soda glass Silica glass Silicon Stone Brick ABS Epoxies Ionomers MFA, 04 Design guidelines

Toughness Gc = (K1C)2/E kJ/m2

Lower limit for K1C K1C / E

(K1C)2/ E

Figure 4.7 Fracture toughness,KIC, plotted against Young’s modulus,E The family of lines are of

constantK2IC=E(approximatelyGIC, the fracture energy or toughness) These, and

the guideline of constantKIC/E, help in design against fracture The shaded band shows

the ‘‘necessary condition’’ for fracture Fracture can, in fact, occur below this limit under conditions of corrosion, or cyclic loading

(72)

or the release of elastic energy stored in the special dislocation structures caused by fatigue loading, is available, when it is given a new symbol such as (K1)scc meaning ‘‘the critical value of K1 for stress-corrosion cracking’’ or

(K1)threshold meaning ‘‘the minimum range ofK1 for fatigue-crack propaga-tion’’ We note that the brittlest ceramics lie close to the threshold: when they fracture, the energy absorbed is only slightly more than the surface energy When metals and polymers and composites fracture, the energy absorbed is vastly greater, usually because of plasticity associated with crack propagation We come to this in a moment, with the next chart

Plotted on Figure 4.7 are contours of toughness, G1C, a measure of the apparent fracture surface-energyðG1CK21C=EÞ The true surface energies,, of solids lie in the range 104to 103kJ/m2 The diagram shows that the values of the toughness start at 103kJ/m2and range through almost five decades to over 100 kJ/m2 On this scale, ceramics (103–101kJ/m2) are much lower than polymers (101–10 kJ/m2); and this is part of the reason polymers are more widely used in engineering than ceramics This point is developed further in Chapter 6, Section 6.10

The fracture toughness–strength chart

The stress concentration at the tip of a crack generates aprocess-zone: a plastic zone in ductile solids, a zone of micro-cracking in ceramics, a zone of delami-nation, debonding and fiber pull-out in composites Within the process zone, work is done against plastic and frictional forces; it is this that accounts for the difference between the measured fracture energy G1C and the true surface energy The amount of energy dissipated must scale roughly with the strength of the material within the process zone, and with its size,dy This size is found by equating the stress field of the crackẳK=p2rịatrẳdy/2 to the strength of the material,f, giving

dyẳ

K2 1C

2f 4:9ị

Figure 4.8 — fracture toughness against strength — shows that the size of the zone, dy(broken lines), varies enormously, from atomic dimensions for very brittle ceramics and glasses to almost m for the most ductile of metals At a constant zone size, fracture toughness tends to increase with strength (as expected): it is this that causes the data plotted in Figure 4.8 to be clustered around the diagonal of the chart

Materials towards the bottom right have high strength and low toughness; theyfracture before they yield Those towards the top left the opposite: they yield before they fracture

(73)

The loss coefficient–modulus chart

Bells, traditionally, are made of bronze They can be (and sometimes are) made of glass; and they could (if you could afford it) be made of silicon carbide Metals, glasses and ceramics all, under the right circumstances, have low intrinsic damping or ‘‘internal friction’’, an important material property when structures vibrate Intrinsic damping is measured by the loss coefficient, , which is plotted in Figure 4.9

There are many mechanisms of intrinsic damping and hysteresis Some (the ‘‘damping’’ mechanisms) are associated with a process that has a specific time constant; then the energy loss is centered about a characteristic frequency Others (the ‘‘hysteresis’’ mechanisms) are associated with time-independent mechanisms; they absorb energy at all frequencies In metals a large part of the loss is hysteretic, caused by dislocation movement: it is high in soft metals like

Elaaststiic lic limmiit,t σσff((MMPPaa)

F rra ct u re to u g h n e ss , K1 KK CC ((M P a mm /2//)

0.11 1010 100 1000

0.0011 0.1 10 100 1000 100 10 0.1 0.01 1000 Guidelines for safe design

Yield before fracture Fracture before yield Process zone size, mm Non-technical ceramics Foams Polymers and elastomers Metals Technical ceramics s Compositess Lead alloys

W alloyss Stainless steelsa s st

Ti alloys Ti a Mg alloys CFRP CFR GFRP G Al alloys Rigid polymer foams Flexible polymerble p

foamsoam

Ni alloys Cu alloysy

Zinc alloysy

PMMA P P P P Corkrk Wood Woo

Butyl rubberyl ru Silicone e elastomersome Concreteonc

Al22O3 SiC Si3N4

Fracture toughness - Strength

B4C

Neoprene Isoprene Leather Cast C irons WC WC

Soda glassa

Silica glass Silicon Stone Ston Brickk ABSBS A A A Epoxiesx E Ionomersrs

Low alloy steels L eels Carbon Ca steels Polyurethanen PA PA PA PA PC P PE PE PE PTFEEE P P P P P P PS PS PSSS P P P P P PPPP

henolice h li Ph Phhhh

MFA, 04

K1

K KC/ σf

((KKK1C)22/ σff

Figure 4.8 Fracture toughness,KIC, plotted against strength,f The contours show the value of

K2

IC=f— roughly, the diameter of the process-zone at a crack tip The design guidelines are used in selecting materials for damage-tolerant design

4.3 The material property charts 61

(74)

lead and pure aluminum Heavily alloyed metals like bronze and high-carbon steels have low loss because the solute pins the dislocations; these are the materials for bells Exceptionally high loss is found in the Mn–Cu alloys, because of a strain-induced martensite transformation, and in magnesium, perhaps because of reversible twinning The elongated bubbles for metals span the large range made accessible by alloying and work hardening Engineering ceramics have low damping because the enormous lattice resistance pins dis-locations in place at room temperature Porous ceramics, on the other hand, are filled with cracks, the surfaces of which rub, dissipating energy, when the material is loaded; the high damping of some cast irons has a similar origin In polymers, chain segments slide against each other when loaded; the relative motion dissipates energy The ease with which they slide depends on the ratio of the temperatureT(in this case, room temperature) to the glass temperature,

Tg, of the polymer When T/Tg<1, the secondary bonds are ‘‘frozen’’, the modulus is high and the damping is relatively low When T/Tg>1,

Yo Y

Y uunngg's mos modduulluus, s EEEE((GGPPaa)

L o ss co co ee ffff iicici ee nn tt, ηη, at 30a oC 1000 10

10-3 10-2 10-1 11 10 100

10-55 10-4 10-3 10-2 10-1 10 Foamsm Polymers Metals Technical ceramics Composites Lead alloys W alloys Steels Ti alloys Mg alloysl

CFRP GFRPF Al alloys Cast irons Cu alloys Zinc alloys PS PS PMMA Epoxies Epoxies PET Cork Woodd Silicone elastomers Concrete WC Al2O3

SiC

Si Si3NN4 Loss coefficient - Modulus

Rigid polymery foams Flexible polymer foams ABS PTFEE Polyurethanee Butyl rubber EVA Neoprene Isoprene Leather PE Ionomers PP PC Soda glass Silica glass Non-technical ceramics Brick Stone MFA, 04 E

e ηE = 0.04 GPa

Elastomers

Figure 4.9 The loss coefficient,, plotted against Young’s modulus,E The guideline corresponds to the condition¼CE

(75)

the secondary bonds have melted, allowing easy chain slippage; the modulus is low and the damping is high This accounts for the obvious inverse dependence ofon Efor polymers in Figure 4.9; indeed, to a first approximation,

¼410

2

E ð4:10Þ

(withEin GPa) for polymers, woods and polymer–matrix composites

The thermal conductivity–electrical resistivity chart

The material property governing the flow of heat through a material at steady-state is the thermal conductivity, (units: W/m.K) The valence electrons in metals are ‘‘free’’, moving like a gas within the lattice of the metal Each electron carries a kinetic energy3

2kT, and it is the transmission of this energy,

via collisions, that conducts heat The thermal conductivity is described by

ẳ1

3Cecc 4:11ị

whereCeis the electron specific heat per unit volume,ccis the electron velocity (2105m/s) and the electron mean-free path, typically 107m in pure metals In heavily alloyed solid solution (stainless steels, nickel-based super-alloys, and titanium alloys) the foreign atoms scatter electrons, reducing the mean free path to atomic dimensions (1010m), much reducing

These same electrons, when in a potential gradient, drift through the lattice, giving electrical conduction The electrical conductivity,, here measured by its reciprocal, theresistivitye(SI units:.m, units of conveniencem.cm) The range is enormous: a factor of 1028, far larger than that of any other property As with heat, the conduction of electricity is proportional to the density of carriers (the electrons) and their mean-free path, leading to the WiedemannFranz relation

/ẳ

e

4:12ị

The quantitiesandeare the axes of Figure 4.10 Data for metals appear at the top left The broken line shows that the Wiedemann–Franz relation is well obeyed

But what of the rest of the chart? Electrons not contribute to thermal conduction in ceramics and polymers Heat is carried by phonons–lattice vibrations of short wavelength They are scattered by each other (through an anharmonic interaction) and by impurities, lattice defects, and surfaces; it is these that determine the phonon mean-free path, The conductivity is still given by equation (4.11), which we write as

ẳ1

3Cpcc 4:13ị

(76)

but nowccis the elastic wave speed (around 103m/s — see Figure 4.3),is the density andCp3is thespecific heat per unit mass(units: J/kg.K) If the crystal is particularly perfect and the temperature is well below the Debye temperature, as in diamond at room temperature, the phonon conductivity is high: it is for this reason that single crystal silicon carbide and aluminum nitride have thermal conductivities almost as high as copper The low conductivity of glass is caused by its irregular amorphous structure; the characteristic length of the molecular linkages (about 109m) determines the mean free path Polymers have low conductivities because the elastic wave speedccis low (Figure 4.3), and the mean free path in the disordered structure is small Highly porous materials like firebrick, cork and foams show the lowest thermal con-ductivities, limited by that of the gas in their cells

s Foams Polymers and Polymers an elastomers Metals Technical ceramics

Compositesmm

Natural materials Lead alloysll

W alloysyy

Steelsee

Ti alloysaa Mg alloysoy

CFRPFF

GFRPRR G GFR GF Al alloysss

Rigid polymer foams

FlexibleFF polymer foamsmm Cu alloysys

Zn alloysyy

PAAA

PMMA PET P P Corkrr Wood Butyl rubber Concrete Tungstenee

carbideee

Al2O333 SiC

Si Si Si333333NNN444

T-Conductivity - Resistivity

Stainlessl steelssteelssteelssteelseeee

Al nitridenn Siliconl

PP PS

PE Glass ss

ceramicmm

Leatherrr Boron carbide Neoprene 1000 100 10 0.1 0.01

1 104 108 1012 1016 1020 1024 1028

Electrical resistivity,ρe (µ-Ω.cm)

Ther mal conductivity , λ (W/m.K ) Stone Glasses Silica glassss Sodaoo

glassaa

MFA, 04 Line of λ= C///ρe

Figure 4.10 Thermal conductivity,, plotted against electrical resistivity,e For metals the two are

(77)

Graphite and many intermetallic compounds such as WC and B4C, like metals, have free electrons, but the number of carriers is smaller and the resistivity higher Defects such as vacancies and impurity atoms in ionic solids create positive ions that require balancing electrons These can jump from ion to ion, conducting charge, but slowly because the carrier density is low Covalent solids and most polymers have no mobile electrons and are insulators (e>1012 m.cm) — they lie on the right-hand side of Figure 4.10

Under a sufficiently high potential gradient, anything will conduct The gradient tears electrons free from even the most possessive atoms, accelerating them into collision with nearby atoms, knocking out more electrons and creating a cascade The critical gradient is called the breakdown potential Vb (units: MV/m), defined in Chapter

The thermal conductivity–thermal diffusivity chart

Thermal conductivity, as we have said, governs the flow of heat through a material at steady-state The property governing transient heat flow is the

thermal diffusivity,a(units: m2/s) The two are related by

aẳ Cp

4:14ị

wherein kg/m3is the density The quantityCpis thevolumetric specific heat (units: J/m3.K) Figure 4.11 relates thermal conductivity, diffusivity and volumetric specific heat, at room temperature

The data span almost five decades inanda Solid materials are strung out along the line4

Cp3106J=m3:K ð4:15Þ

As a general rule, then,

ẳ3106a 4:16ị

(in W/m.K andain m2/s) Some materials deviate from this rule: they have lower-than-average volumetric specific heat The largest deviations are shown

4 This can be understood by noting that a solid containing N atoms has 3N vibrational modes Each (in the classical approximation) absorbs thermal energykTat the absolute temperatureT, and the vibrational specific heat isCpCv¼3N/k(J/K) wherekis Boltzmann’s constant (1.341023J/K) The volume per atom,, for almost all solids lies within a factor of two of 1.41029m3; thus the volume ofNatoms is (NCp) m3 The volume specific heat is then (as the Chart shows):

Cvﬃ3Nk=N¼

3k

¼310

6J=m3:K

(78)

by porous solids: foams, low density firebrick, woods, and the like Their low density means that they contain fewer atoms per unit volume and, averaged over the volume of the structure,Cpis low The result is that, although foams have low conductivities(and are widely used for insulation because of this), their thermaldiffusivitiesare not necessarily low: they may not transmit much heat, but they reach a steady-state quickly This is important in design — a point brought out by the Case Study of Section 6.13

The thermal expansion–thermal conductivity chart

Almost all solids expand on heating The bond between a pair of atoms behaves like a linear elastic spring when the relative displacement of the atoms is small, but when it is large, the spring is non-linear Most bonds become

T

Thheerrmmaall ddiiffffuusisivviitty, y aa((mm22//s)//

T h e rm a l co n d u c ti v it y, λ (W / W mm K ) 10

10 10-7 1010-6 10-5 10-4

0.0011 0.1 10 100 1000 107 Guidelines for thermal design High volumetric specific heat Low volumetric specific heat 106 105

Vol specific heat ρCCpp (J/m3.K)

λ a λ a1/2 Foams Polymers and elastomers Metals Technical ceramics Compositesites Lead alloys W alloys W Carbon steels

Ti alloyso

Mg alloysl

CFRP

GFRP

Al alloys

Rigid polymerme foamsams

Flexible polymer Fl ibl l

foams Ni alloys Cu alloys Zn alloys PTFE PTF PC PC Cork Wood Butyl rubber Silicone elastomerss Concretencre Al Al22OO33

SiC

Si3N4

T-conductivity - T-diffusivity

B4C

PP Isoprene call Non-technic ceramics MFA, 04 Cast irons WC

Soda glassda Stonene Brick B Epoxies E E Stainless steels AlN A Silicon Neoprene N PMMAMM PVC PVC

Figure 4.11 Thermal conductivity,, plotted against thermal diffusivity,a The contours show the volume specific heat,Cv All three properties vary with temperature; the data here are

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stiffer when the atoms are pushed together, and less stiff when they are pulled apart, and for that reason they are anharmonic The thermal vibrations of atoms, even at room temperature, involves large displacements; as the temperature is raised, the anharmonicity of the bond pushes the atoms apart, increasing their mean spacing The effect is measured by the linearexpansion coefficient

¼1

l

dl

dT ð4:17Þ

wherelis a linear dimension of the body

The expansion coefficient is plotted against the thermal conductivity in Figure 4.12 It shows that polymers have large values of, roughly 10 times greater than those of metals and almost 100 times greater than ceramics This is

T

Thheerrmmaall coconndduuctctiivviitty, y,λλ ((WW//WWW mm.K)

0 0011

T h e rm a ll ex p a n i s io n, α ((µ t s tr a iin /K ) 0.11 1

0.1 1010 100 1000

1 10 100 1000 = 10 = =

Large thermal strain mismatch

Small thermal strain mismatch λ

αα (W/m)

λ αα (W/m)

1044 105 106

106 107 =10 = 104 105 Foams Polymers and elastomers Metals Techncial ceramics Composites Natural materials

Lead alloysead alloys Lead L Lead Le Lead L W alloys Steelss Ti alloys

Mg alloysoys

CFRP GFRP G

Al alloys Al

Rigid polymerigid foams Flexible polymer

foams

Ni alloyso Ni a

Cu alloys Zn alloysn

PA PA PMMAM P P P A PC PET Wood Butyl rubbery Silicone elastomerser Concrete C WC

Al2OO3 SiC

Si33NN4

T- expansion - T- conductivity

Pb alloys Stainlessn steelse Silica glassss Silicon AlN Soda glasss Neoopreneo PEE Epoxies Ep ABS AB E

MFA, 044

Invar

Figure 4.12 The linear expansion coefficient,, plotted against the thermal conductivity, The contours show the thermal distortion parameter/ An extra material, the nickel alloy Invar, has been added to the chart; it is noted for its exceptionally low expansion at and near room temperature, useful in designing precision equipment that must not distort if the temperature changes

(80)

because the Van-der-Waals bonds of the polymer are very anharmonic Diamond, silicon, and silica glass (SiO2) have covalent bonds that have low anharmonicity (i.e they are almost linear-elastic even at large strains), giving them low expansion coefficients Composites, even though they have polymer matrices, can have low values ofbecause the reinforcing fibers — particularly carbon — expand very little

The chart shows contours of/, a quantity important in designing against thermal distortion An extra material, Invar (a nickel alloy) has been added to the chart because of its uniquely low expansion coefficient at and near room temperature, an consequence of a trade-off between normal expansion and a contraction associated with a magnetic transformation An application that uses chart is developed in Chapter 6, Section 6.16

The thermal expansion–modulus chart

Thermal stress is the stress that appears in a body when it is heated or cooled but prevented from expanding or contracting It depends on the expansion coefficient, , of the material and on its modulus, E A development of the theory of thermal expansion (see, e.g., Cottrell, 1964) leads to the relation

ẳGCp

3E 4:18ị

whereGis Gruneisens constant; its value ranges between about 0.4 and 4, but for most solids it is near SinceCpis almost constant (equation (4.15)), the equation tells us that is proportional to 1/E Figure 4.13 shows that this is broadly so Ceramics, with the highest moduli, have the lowest coefficients of expansion; elastomers with the lowest moduli expand the most Some ma-terials with a low co-ordination number (silica, and some diamond-cubic or zinc-blende structured materials) can absorb energy preferentially in transverse modes, leading to very small (even a negative) value ofGand a low expansion coefficient — silica, SiO2, is an example Others, like Invar, contract as they lose their ferromagnetism when heated through the Curie temperature and, over a narrow range of temperature, they too show near-zero expansion, useful in precision equipment and in glass–metal seals

One more useful fact: the moduli of materials scale approximately with their melting point,Tm:

E100kTm

O ð4:19Þ

wherekis Boltzmann’s constant andOthe volume-per-atom in the structure Substituting this and equation (4.15) forCpinto equation (4.18) forgives

¼ G

100Tm

(81)

the expansion coefficient varies inversely with the melting point, or (equiva-lently stated) for all solids the thermal strain, just before they melt, depends only on G, and this is roughly a constant Equations (4.18) and (4.19) are examples of property correlations, useful for estimating and checking material properties (Chapter 15)

Whenever the thermal expansion or contraction of a body is prevented, thermal stresses appear; if large enough, they cause yielding, fracture, or elastic collapse (buckling) It is common to distinguish between thermal stress caused by external constraint (e.g a rod, rigidly clamped at both ends) and that which appears without external constraint because of temperature gradients in the body All scale as the quantity E, shown as a set of diagonal contours in Figure 4.13 More precisely: the stressproduced by a temperature change

Yo Y

Y ung's modulus, E (GPa)

T h e rm a l e x p a n s io n, α (µ s tr a in /K )

0 001 0.1 10 100 1000

1 10 100 1000

αE(MPa/K) = 10 10 0.1 0.1 0.01 0.01 Foams Polymers Elastomers Metals Technical ceramics Composites Leada alloysoy W alloys W Steelsee

Ti alloyso Ti a Mg alloys CFRP CFRP GFRP GF

Al alloysallo

Cast ironsst Cu alloysa Zinc alloysn s

PS PMMAMMA

Epoxies PETE Corkk

Wood Siliconesc s

Concreteee

WC All222OOO33

AlN AlN

Si33N4

T-expansion - Modulus

Rigid polymerg p yy foams Flexible polymero

foams ABS PTFE Polyurethane P EVA Isoprene Leather Leatherrr PE Ionomersrsssssss PP

PC P as a a assss a as a as a Sodaglaaaa

Silica glass Si

Non-technical

ceramics Stonen Brick

MFA, 04

SiC S

B44C

Siliconlico Acetal A Phenolico PEEK Natural materials a a a as a as a a a a a a

Figure 4.13 The linear expansion coefficient,, plotted against Young’s modulus,E The contours show the thermal stress created by a temperature change of 1C if the sample is axially constrained A correction factorCis applied for biaxial or triaxial constraint

(see text)

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of 1C in a constrained system, or the stress perC caused by a sudden change of surface temperature in one that is not constrained, is given by

C¼E 4:21ị

where Cẳ1 for axial constraint, (1v) for biaxial constraint or normal quenching, and (12v) for triaxial constraint, wherevis Poisson’s ratio These stresses are large: typically MPa/K They can cause a material to yield, or crack, or spall, or buckle when it is suddenly heated or cooled

The strength–maximum service temperature chart

Temperature affects material performance in many ways As the temperature is raised the material may creep, limiting its ability to carry loads It may degrade or decompose, changing its chemical structure in ways that make it unusable And it may oxidize or interact in other ways with the environment in which it is used, leaving it unable to perform its function The approximate temperature at which, for any one of these reasons, it is unsafe to use a material is called its

maximum service temperature Tmax Figure 4.14 shows this plotted against strength

The chart gives a birds-eye view of the regimes of stress and temperature in which each material class, and material, is usable Note that even the best polymers have little strength above 200C; most metals become very soft by 800C; and only ceramics offer strength above 1500C.

Friction and wear

God, it is said, created solids, but it was the devil that made surfaces — they are the source of many problems When surfaces touch and slide, there is friction; and where there is friction, there is wear Tribologists — the collective noun for those who study friction and wear — are fond of citing the enormous cost, through lost energy and worn equipment, for which these two phenomena are responsible It is certainly true that, if friction could be eliminated, the effi-ciency of engines, gear boxes, drive trains and the like would increase; and if wear could be eradicated, they would also last longer But before accepting this negative image, one should remember that, without wear, pencils would not write on paper or chalk on blackboards; and without friction, one would slither off the slightest incline

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(for which see Chapter 15); in the end it is these that must be consulted But it does help to have a feel for the magnitude of friction coefficients and wear rates, and an idea of how these relate to material class

When two surfaces are placed in contact under a normal loadFnand one is made to slide over the other, a force Fs opposes the motion This force is proportional toFnbut does not depend on the area of the surface — and this is the single most significant result of studies of friction, since it implies that surfaces not contact completely, but only touch over small patches, the area of which is independent of the apparent, nominal area of contact An The

coefficient frictionis defined by

ẳFs Fn

4:22ị

Maximmuumm seserrvrrr iicevce tetemmppeerraattuurre, Te, Tmaxmax((˚C)

Strength, en g th , σf ((MM PP a )) 0.001 0.1 10 100 1000

100 30 110000 300300 1000

Foams Polymers and elastomers Metals Technical ceramics Lead alloys W alloys Stainless steels Ti alloys

Mg alloysg CFRP GFRP Al alloys Al alloys Cast irons Cu alloys Zinc alloys PMMAA PMMA Epoxies Epoxies PET P Cork Wood Siliconen elastomersm elastomers Concreten AlN Al2O3 SiC Si3N4

Strength - Max service temp.

Rigid polymer foams Flexible polymer foams ABS Butyl rubberr EVA Neoprene Leatherrr Ionomers PP oda glass Soda goda goda g

Silica glass

Non-technical ceramics

Brick B i k

MFA, 04

Carbon steels

Ni alloyso Low alloy

steels

B4C

Stone orosilicate glassa

Borosilicate B Bo Bo Borosilicate g Borosilicate PTFE PEEK Nylons PVC T

Figure 4.14 Strength plotted against maximum service temperature

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Approximate values forfor dry — that is, unlubricated—sliding of materials on a steel counterface are shown in Figure 4.15 Typically, 0.5 Certain materials show much higher values, either because they seize when rubbed together (a soft metal rubbed on itself with no lubrication, for instance) or because one surface has a sufficiently low modulus that it conforms to the other (rubber on rough concrete) At the other extreme are sliding combinations with exceptionally low coefficients of friction, such as PTFE, or bronze bearings loaded graphite, sliding on polished steel Here the coefficient of friction falls as low as 0.04, though this is still high compared with friction for lubricated surfaces, as noted at the bottom of the diagram

When surfaces slide, they wear Material is lost from both surfaces, even when one is much harder than the other Thewear-rate,W, is conventionally defined as

W¼Volume of material removed from contact surface

Distance slid ð4:23Þ

and thus has units of m2 A more useful quantity, for our purposes, is the specific wear-rate

O¼W An

4:24ị

Coefficient of friction on dry steel,

à

0.01 0.1 10

Lead alloys

Low carbon steels

Al alloys Cu alloys

PA

PMMA

Wood Butyl rubber

Cast irons WC

Coefficient of friction

PTFE Leather

MFA, 04

PP

PE Soda glass

Natural rubber

Borosilicate glass

PS

NOTE: µ for partial lubrication = 0.01 0.1

µ for full hydrodyamic lubrication = 0.001 0.01

(85)

which is dimensionless It increases with bearing pressureP(the normal force

Fndivided by the nominal areaAn), such that the ratio

kaẳ

W Fn

ẳO

P 4:25ị

is roughly constant The quantityka(with units of (MPa)1) is a measure of the propensity of a sliding couple for wear: high kameans rapid wear at a given bearing pressure

The bearing pressurePis the quantity specified by the design The ability of a surface to resist a static contact pressure is measured by its hardness, so we anticipate that the maximum bearing pressure Pmax should scale with the hardnessHof the softer surface:

Pmax¼CH

whereCis a constant Thus the wear-rate of a bearing surface can be written: O¼kaP¼C

P Pmax

kaH ð4:26Þ

Two material properties appear in this equation: the wear constantkaand the hardness, H They are plotted in Figure 4.16 The dimensionless quantity

KẳkaH 4:27ị

is shown as a set of diagonal contours Note, first, that materials of a given class (for instance, metals) tend to lie along a downward sloping diagonal across the figure, reflecting the fact that low wear rate is associated with high hardness The best materials for bearings for a given bearing pressure Pare those with the lowest value of ka, that is, those nearest the bottom of the diagram On the other hand, an efficient bearing, in terms of size or weight, will be loaded to a safe fraction of its maximum bearing pressure, that is, to a constant value ofP/Pmax, and for these, materials with the lowest values of the productkaHare best

Cost bar charts

Properties like modulus, strength or conductivity not change with time Cost is bothersome because it does change with time Supply, scarcity, speculation and inflation contribute to the considerable fluctuations in the cost-per-kg of a commodity like copper or silver Data for cost-per-kg are tabulated for some materials in daily papers and trade journals; those for others are harder to come by Approximate values for the cost of materials per kg, and their cost per m3, are plotted in Figure 4.17(a) and (b) Most commodity materials (glass, steel, aluminum, and the common polymers) cost between $0.5 and $2/kg Because

(86)

they have low densities, the cost/m3of commodity polymers is less than that of metals

The modulus–relative cost chart

In design for minimum cost, material selection is guided by indices that involve modulus, strength, and cost per unit volume To make some correction for the influence of inflation and the units of currency in which cost is measured, we define arelative cost per unit volume Cv,R

Cv;R¼

Cost=kgDensity of material

Cost=kgDensity of mild steel rod ð4:28Þ

At the time of writing, steel reinforcing rod costs about US$0.3/kg

Haarrddnneess, H ss H ((MMPa)

W e aa rr-rraa ttee coco nn stst aa nn tt k , k tt aa ((11 //(( MM PP a ))

100 100 11000000 10,000 100,000

100-1111 10-10 10 -9 10 -8 10 -7 10 -6 10-5 10-4 10-6 10-7 10-5 10-4

10-3 Dimensionless wear contant K = kkk Ha

Polymers and elastomers Metals Technical ceramics Stainless steels Al alloys

Cu alloysys

PMMAM

Al2O3

SiC

Wear rate - Hardness

Cast irons

WC

Silica glass Silica

Low alloy steels

Tool steels Low carbon steels PA PC PE PTFE PP MFA, 04

Medium carbon m steels s

High carbon steels g Bronze Filled thermoplastics Unfilled thermoplastics

Figure 4.16 The normalized wear rate,ka, plotted against hardness,H, here expressed in MPa rather

than Vickers (Hin MPa¼10Hv) The chart gives an overview of the way in which

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Material class

Approximate cost per unit volume

($/ m 3) 102 103 104 105 106

Ceramics Composites Metals Polymers Aluminum nitride Boron carbide Silicon nitride Tungsten carbide Silicon carbide Silicon Silica glass Borosilicate glass Alumina Soda glass Brick Stone Concrete CFRP GFRP Titanium alloys Tungsten alloys Nickel alloys Stainless steel Magnesium alloys Copper alloys Zinc alloys Aluminum alloys Lead alloys

Low alloys steels Carbon steels Cast irons PEEK PTFE Silicone Polyurethane PC CA Epoxy ABS EVA PE PET POM Nylon Neoprene PMMA PS PVC PP Butyl rubber MFA, 04 Material class (a) (b)

Approximate cost per unit mass

($/

kg

)

Ceramics Composites Metals Polymers 0.01 0.1 10 100 Aluminum nitride Boron carbide Silicon nitride Tungsten carbide Silicon carbide Silicon Silica glass Borosilicate glass Alumina Soda glass Brick Stone Concrete CFRP GFRP Titanium alloys Tungsten alloys Nickel alloys Stainless steel Magnesium alloys Copper alloys Zinc alloys Aluminum alloys Lead alloys Low alloys steels

Carbon steels Cast irons PEEK PTFE Silicone Polyurethane PC CA Epoxy ABS EVA PE PET POM Nylon Neoprene

PMMAPSPVC PP

Butyl rubber

MFA, 04

Figure 4.17 (a) The approximate cost/kg of materials Commodity materials cost about $1/kg special materials cost much more (b) The approximate cost/m3of materials Polymers, because they have low densities, cost less per unit volume than most other materials

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Figure 4.18 shows the modulus E plotted against relative cost per unit volumeCv,Rwhereis the density Cheap stiff materials lie towards the top left Guidelines for selection materials that are stiff and cheap are plotted on the figure

The strength–relative cost chart

Cheap strong materials are selected using Figure 4.19 It shows strength, defined as before, plotted against relative cost per unit volume, defined above The qualifications on the definition of strength, given earlier, apply here also It must be emphasized that the data plotted here and on the chart of Figure 4.18 are less reliable than those of other charts, and subject to unpredictable change Despite this dire warning, the two charts are genuinely useful They allow selection of materials, using the criterion of ‘‘function per unit cost’’ An example is given in Chapter 6, Section 6.5

Relaattiivvevvvv coecostst ppeerr uunniitt vvovvvv lluoumme, Ce Cv,R

Y oo u nn gg ''sm o s mo dd u llu sEs, E ((GG PP a )

0.001 0.1 11 1010 100

0.001 0.1 10 100 1000 E1/3 Cv,Rv,R

E1/2 Cv,R E Cv,R Guidelines for minimum cost design Foams olymers

Pooo

Polymers Metalss Technical ceramics Compositese Natural materials

Leadead alloyseadeadaaa

W alloys Carbon steelss

Ti alloysi

Mg alloyssss CFRP

GFRP Al alloys Al alloys Rigid polymer foams Flexible polymer foamsfoams Zinc alloys PS PTFE PC Wood Siliconelic elastomers ela s Concrete

Al2O3

SiC Si33N44 Modulus - Relative cost/vol

B44C

PP EVA Polyurethanee Leather Non-technical ceramicsceramics MFA, 04 Cast irons WC Soda glass Sil Silica glassg Sil Sil

Silicon

Stonen Brick

ABS Epoxieso Epoxies Ionomers AlN Stainless Stainless steels PEEK PE PE PMMA PM PM PM Polyurethanes Acetal // grain grain T Elastomers

Figure 4.18 Young’s modulus,E, plotted against relative cost per unit volume,Cv,R The design

(89)

The engineering properties of materials are usefully displayed as material selection charts The charts summarize the information in a compact, easily accessible way, they show the range of any given property accessible to the designer and they identify the material class associated with segments of that range By choosing the axes in a sensible way, more information can be displayed: a chart of modulus E against density reveals the long-itudinal wave velocity (E/)1/2; a plot of fracture toughness K1C against

modulus E shows the toughness G1C; a diagram of thermal conductivity

against diffusivity, a, also gives the volume speciﬁc heat Cv; strength, f,

against modulus, E, shows the energy-storing capacity 2f=E, and there are many more

The most striking feature of the charts is the way in which members of a material class cluster together Despite the wide range of modulus and density

Strength,St ren gth, σf ((MM PP a ))

0.001 0.1 11 1010 1000

0.001 0.1 10 100 1000 10000

Relativev cov costst ppeerr uunniitt vv lluvovvvoumme, Ce Cv,RR Foams Polymers and elastomers Metals Technical ceramics Compositesp Natural materials Lead alloys W alloys Carbon steels Ti alloys Mg alloys M CFRP GFRP Al alloys Rigid polymer foams Flexible polymolymerolymolym foamssss

Cu alloys Zinc alloys PS PTFE Cork Wood

Silicone o elastomerso Concrencretencrencre

Al2O3 SiC Si3N4 Strength - Relative cost/vol

e

B4C

PP

Neolprenen Leather Non-technical

ceramics

MFA, 04,

Cast irons WC Silica glass Silicon Stone Brick B ABS ABS E Epoxies Ep Ep

Ionomersmersmersmers

AlN Stainless steels PEEKK PE // grain grain gra T T σf 1/2 1/2 f Cv,R σf 2/3 f Cv,R σff Cv,R Guidelines for minimum cost design

Figure 4.19 Strength,f, plotted against relative cost per unit volume,Cv,R The design guidelines help

selection to maximize strength per unit cost

(90)

of metals (as an example), they occupy a field that is distinct from that of polymers, or that of ceramics, or that of composites The same is true of strength, toughness, thermal conductivity and the rest: the fields sometimes overlap, but they always have a characteristic place within the whole picture The position of the fields and their relationship can be understood in simple physical terms: the nature of the bonding, the packing density, the lattice resistance and the vibrational modes of the structure (themselves a function of bonding and packing), and so forth It may seem odd that so little mention has been made of micro-structure in determining properties But the charts clearly show that the first-order difference between the properties of materials has its origins in the mass of the atoms, the nature of the inter-atomic forces and the geometry of packing Alloying, heat treatment, and mechanical working all influence micro-structure, and through this, properties, giving the elongated bubbles shown on many of the charts; but the magnitude of their effect is less, by factors of 10, than that of bonding and structure

All the charts have one thing in common: parts of them are populated with materials and parts are not Some parts are inaccessible for fundamental rea-sons that relate to the size of atoms and the nature of the forces that bind their atoms together But other parts are empty even though, in principle, they are accessible If they were accessed, the new materials that lay there could allow novel design possibilities Ways of doing this are explored further in Chapters 13 and 14

The charts have numerous applications One is the checking and validation of data (Chapter 15); here use is made both of the range covered by the envelope of material properties, and of the numerous relations between them (likeEO¼100kTm), described in Section 4.3 Another concerns the develop-ment of, and identification of uses for, new materials; materials that fill gaps in one or more of the charts generally offer some improved design potential But most important of all, the charts form the basis for a procedure for materials selection That is developed in the following chapters

4.5 Further reading

The best general book on the physical origins of the mechanical properties of materials remains that by Cottrell (1964) Values for the material properties that appear on the Charts derive from sources documented in Chapter 13

Cottrell, A.H (1964)Mechanical Properties of Matter, Wiley, New York Library of Congress Number 65-14262 (An inspirational book, clear, full of insights and of simple derivations of the basic equations describing the mechanical behavior of solids, liquids and gasses.)

(91)

Metals

Elastomers

Ceramics

Woods

Foams

0.1 10

1 100

0.01 1000

100

0.1 10

Density (Mg/m3)

Yo

u

n

g

’s

mo

d

u

lu

s

E (GPa)

Modulus-Density

MFA, 04

Polymers Composites

E1/2/ρ

E1/3/ρ E/ρ

Guide lines for minimum mass

design

1

2 3

E

Chapter contents

5.2 The selection strategy 81

5.3 Attribute limits and material indices 85

5.4 The selection procedure 93

5.5 Computer-aided selection 99

5.6 The structural index 102

Chapter 5

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This chapter sets out the basic procedure for selection, establishing the link

between material and function (Figure 5.1) A material has attributes: its

density, strength, cost, resistance to corrosion, and so forth A design demands a certain profile of these: a low density, a high strength, a modest cost and resistance to sea water, perhaps It is important to start with the full menu of materials in mind; failure to so may mean a missed opportunity If an innovative choice is to be made, it must be identified early in the design process Later, too many decisions have been taken and commitments made to allow radical change: it is now or never The task, restated in two lines, is that of

(1) identifying the desired attribute profile and then

(2) comparing it with those of real engineering materials to find the best match

The first step in tackling it is that of translation, examining the design

requirements to identify the constraints that they impose on material choice

The immensely wide choice is narrowed, first, byscreening-outthe materials

that cannot meet the constraints Further narrowing is achieved byrankingthe

candidates by their ability to maximize performance Criteria for screening and ranking are derived from the design requirements for a component by an

analysis offunction, constraints, objectives, and free variables This chapter

explains how to it

The materials property charts introduced in Chapter are designed for use with these criteria Property constraints and material indices can be plotted onto them, isolating the subset of materials that are the best choice for the

Function

Process

Shape Material

Material families, classes, sub-classes

and members Material attributes

Material limits and indices

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design The whole procedure can be implemented in software as a design tool, allowing computer-aided selection The procedure is fast, and makes for lateral thinking Examples of the method are given in Chapter

5.2 The selection strategy

Material attributes

Figure 5.2 illustrates how the kingdom of materials is divided into families, classes, sub-classes, and members Each member is characterized by a set of

attributes: its properties As an example, the materials kingdom contains the family ‘‘metals’’, which in turn contains the class ‘‘aluminum alloys’’, the sub-class ‘‘6000 series’’ and finally the particular member ‘‘Alloy 6061’’ It, and every other member of the kingdom, is characterized by a set of attributes that include its mechanical, thermal, electrical, optical, and chemical properties, its processing characteristics, its cost and availability, and the environmental

consequences of its use We call this its property-profile Selection involves

seeking the best match between the property-profiles of the materials in the kingdom and that required by the design

There are four main steps, which we here calltranslation, screening, ranking,

andsupporting information(Figure 5.3) The steps can be likened to those in selecting a candidate for a job The job is first analyzed and advertised, iden-tifying essential skills and experience required of the candidate (‘‘translation’’) Some of these are simple go/no go criteria like the requirement that the applicant ‘‘must have a valid driving license’’, or ‘‘a degree in computer science’’,

Materials • • • • • •

Ceramics Glasses Metals Polymers Elastomers Hybrids

Steels Cu-alloys Al-alloys Ti-alloys Ni-alloys Zn-alloys

1000 2000 3000 4000 5000 6000 7000 8000

A material record

Density

Mechanical props Thermal props Electrical props Optical props Corrosion props

Supporting information

specific general

Density

Mechanical props Thermal props Electrical props Optical props Corrosion props

Supporting information

specific general 6013

6060 6061 6063 6082 6151 6463

Family Class Sub-class Member Attributes

Kingdom

Figure 5.2 The taxonomy of the kingdom of materials and their attributes Computer-based selection software stores data in a hierarchical structure like this

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eliminating anyone who does not (‘‘screening’’) Others imply a criterion of excellence, such as ‘‘typing speed and accuracy are priorities’’, or ‘‘preference will be given to candidates with a substantial publication list’’, implying that applicants will be ranked by these criteria (‘‘ranking’’) Finally references and interviews are sought for the top ranked candidates, building a file of sup-porting information — an opportunity to probe deeply into character and potential

Translation

How are the design requirements for a component (defining what it must do) translated into a prescription for a material? Any engineering component has

one or more functions: to support a load, to contain a pressure, to transmit

heat, and so forth This must be achieved subject toconstraints: that certain

Translate design requirements

express as function, constraints, objectives and free variables

All materials

Final material choice

Screen using constraints:

eliminate materials that cannot the job

Rank using objective:

find the screened materials that the job best

Seek supporting information:

research the family history of top-ranked candidates

(95)

dimensions are fixed, that the component must carry the design loads or pressures without failure, that it insulates or conducts, that it can function in a certain range of temperature and in a given environment, and many more In

designing the component, the designer has anobjective: to make it as cheap as

possible, perhaps, or as light, or as safe, or perhaps some combination of these Certain parameters can be adjusted in order to optimize the objective — the designer is free to vary dimensions that have not been constrained by design requirements and, most importantly, free to choose the material for the

component We refer to these as free variables Function and constraints,

objective and free variables (Table 5.1) define the boundary conditions for selecting a material and — in the case of load-bearing components — a shape for its cross-section The first step in relating design requirements to material properties is a clear statement of function, constraints, objective, and free variables

Screening: attribute limits

Unbiased selection requires that all materials are considered to be candidates until shown to be otherwise, using the steps in the boxes below ‘‘translate’’ in

Figure 5.3 The first of these, screening, eliminates candidates that cannot

the job at all because one or more of their attributes lies outside the limits set by the constraints As examples, the requirement that ‘‘the component must function in boiling water’’, or that ‘‘the component must be transparent’’

imposes obvious limits on the attributes ofmaximum service temperatureand

optical transparencythat successful candidates must meet We refer to these as

attribute limits

Ranking: material indices

Attribute limits not, however, help with ordering the candidates that remain To this we need optimization criteria They are found in the material indices, developed below, which measure how well a candidate that

Table 5.1 Function, constraints, objectives and free variables

Function What does component do?

Constraints* What non-negotiable conditions must be met? What negotiable but desirable conditions .? Objective What is to be maximized or minimized?

Free variables What parameters of the problem is the designer free to change? *It is sometimes useful to distinguish between ‘‘hard’’ and ‘‘soft’’ constraints Stiffness and strength might be

absolute requirements (hard constraints); cost might be negotiable (a soft constraint)

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has passed the screening step can the job Performance is sometimes limited by a single property, sometimes by a combination of them Thus the best

materials for buoyancy are those with the lowest density, ; those best for

thermal insulation the ones with the smallest values of the thermal

con-ductivity, Here maximizing or minimizing a single property maximizes

performance But — as we shall see – the best materials for a light stiff tie-rod

are those with the greatest value of the specific stiffness, E/, where E is

Young’s modulus The best materials for a spring are those with the greatest

value of 2f=E wherefis the failure stress The property or property-group

that maximizes performance for a given design is called its material index

There are many such indices, each associated with maximizing some aspect

of performance.1 They provide criteria of excellence that allow ranking of

materials by their ability to perform well in the given application

To summarize: screening isolate candidates that are capable of doing the job; ranking identifies those among them that can the job best

Supporting information

The outcome of the steps so far is a ranked short-list of candidates that meet the constraints and that maximize or minimize the criterion of excellence, whichever is required You could just choose the top-ranked candidate, but what bad secrets might it hide? What are its strengths and weaknesses? Does it have a good reputation? What, in a word, is its credit-rating? To

proceed further we seek a detailed profile of each: itssupporting information

(Figure 5.3, bottom)

Supporting information differs greatly from the structured property data used for screening Typically, it is descriptive, graphical or pictorial: case studies of previous uses of the material, details of its corrosion behavior in particular environments, information of availability and pricing, experience of its environmental impact Such information is found in handbooks, sup-pliers’ data sheets, CD-based data sources and the world-wide web Sup-porting information helps narrow the short-list to a final choice, allowing a definitive match to be made between design requirements and material attributes

Why are all these steps necessary? Without screening and ranking, the candidate-pool is enormous and the volume of supporting information over-whelming Dipping into it, hoping to stumble on a good material, gets you nowhere But once a small number of potential candidates have been identified by the screening–ranking steps, detailed supporting information can be sought for these few alone, and the task becomes viable

1

(97)

Local conditions

The final choice between competing candidates will, often, depend on local conditions: on in-house expertise or equipment, on the availability of local suppliers, and so forth A systematic procedure cannot help here — the decision must instead be based on local knowledge This does not mean that the result of the systematic procedure is irrelevant It is always important to know which material is best, even if, for local reasons, you decide not to use it

We will explore supporting information more fully in Chapter 15 Here we focus on the derivation of property limits and indices

5.3 Attribute limits and material indices

Constraints set property limits Objectives define material indices, for which we seek extreme values When the objective in not coupled to a constraint, the material index is a simple material property When, instead, they are coupled, the index becomes a group of properties like those cited above Both are explained below We start with two simple examples of the first — uncoupled objectives

Heat sinks for hot microchips A microchip may only consume milliwatts,

but the power is dissipated in a tiny volume The power is low but the

power-density is high As chips shrink and clock-speeds grow, heating becomes a

problem The Pentium chip of today’s PCs already reaches 85C, requiring

forced cooling Multiple-chip modules (MCMs) pack as many as 130 chips on to a single substrate Heating is kept under control by attaching the chip to a heat sink (Figure 5.4), taking pains to ensure good thermal contact between the chip and the sink The heat sink now becomes a critical component, lim-iting further development of the electronics How can its performance be maximized?

To prevent electrical coupling and stray capacitance between chip and heat sink, the heat sink must be a good electrical insulator, meaning a resistivity,

Connecting pins Substrate

Chips

Cooling fins Heat sink

Figure 5.4 A heat sink for power micro-electronics The material must insulate electrically, but conduct heat as well as possible

(98)

e>1019m:cm But to drain heat away from the chip as fast as possible, it

must also have the highest possible thermal conductivity, The translation

step is summarized in Table 5.2, where we assume that all dimensions are constrained by other aspects of the design

To explain: resistivity is treated as a constraint, a go/no go criterion

Materials that fail to qualify as ‘‘good insulator’’, or have a resistivity greater than the value listed in the table, are screened out The thermal conductivity is

treated as anobjective: of the materials that meet the constraint, we seek those

with the largest values ofand rank them by this — it becomes the material

index for the design If we assume that all dimensions are fixed by the design,

there remains only one free variable in seeking to maximize heat-flow: the

choice of material The procedure, then, is toscreenon resistivity, thenrankon

conductivity

The steps can be implemented using the e chart of Figure 4.10,

reproduced as Figure 5.5 Draw a vertical line ate¼1019m.cm, then pick

off the materials that lie above this line, and have the highest The result:

aluminum nitride, AlN, or alumina, Al2O3 The final step is to seek

sup-porting information for these two materials A web-search on ‘‘aluminum nitride’’ leads immediately to detailed data-sheets with the information we seek

Materials for overhead transmission lines Electrical power, today, is gener-ated centrally and distributed by overhead or underground cables Buried lines are costly so cheaper overhead transmission (Figure 5.6) is widely used A large span is desirable because the towers are expensive, but so too is a low electrical resistance to minimize power losses The span of cable between two towers must support the tension needed to limit its sag and to tolerate wind and ice

loads Consider the simple case in which the tower spacing L is fixed at a

distance that requires a cable with a strength f of at least 80 MPa (a

con-straint) The objective then becomes that of minimizing resistive losses, and

that means seeking materials with the lowest possible resistivity,e, defining

the material index for the problem The translation step is summarized in Table 5.3

The prescription, then, is toscreenon strength andrankon resistivity There

is no fe chart in Chapter (though it is easy to make one using the

Table 5.2 Function, constraints, objective, and free variables for the heat sink

Function Heat sink

Constraints Material must be ‘‘good insulator’’, ore>1019m cm All dimensions are specified

(99)

software described in Section 5.5) Instead we use the e chart of

Figure 4.10 to identify materials with the lowest resistivity (Cu and Al alloys)

and then check, using thefchart of Figure 4.4 that the strength meets the

constraint listed in the table Both (try it!) L

Transmission

line Tower

Figure 5.6 A transmission line The cable must be strong enough to carry its supporting tension, together with wind and ice loads But it must also conduct electricity as well as possible

λ s Foams P Polymers an elastomers Metals Technical ceramics

Compositesmm

Natural materials W alloysyy

Steelsee

Ti alloysaa Mg alloysoy

CFRPFF

GFRPRR GFRR GF Al alloysss

Rigid polymer foams

Flexible FF polymer foamsmm Cu alloysys

Zn alloysyy

PAAA

PMMA PET P P Corkrr Wood Butyl rubber Concrete Tungstenee

carbideee

Al2O333 SiC

Si Si Si3333NNN444

T-Conductivity - Resistivity

Stainless l steelssteelssteelsee

Al nitridenn Siliconl

PP PS PE Glass ss

ceramicmm

Leatherrr Boron carbide Neoprene 1000 100 10 0.1 0.01

1 104 108 1012 1016 1020 1024 1028

Electrical resistivity,ρe(µ-Ω.cm)

Ther mal conductivit y, λ ( W /m.K ) Stone Glasses

Silica glassss Sodaoo

glassaa

MFA, 04 Line of

λ = C///ρe

Lead alloysll

d n s

ρe = 1019µΩ.cm

Figure 5.5 Theechart of Figure 4.10 with the attribute limite>1019m.cm and the index

plotted on it The selection is reﬁned by raising the position of theselection line

(100)

The two examples have been greatly simplified — reality is more complex than this We will return to both again later The aim here is simply to intro-duce the disciplined way of approaching a selection problem by identifying its key features: function, constraints, objective, and free variables Now for some slightly more complex examples

Material indices when objectives are coupled to constraints

Think for a moment of the simplest of mechanical components, helped by Figure 5.7 The loading on a component can generally be decomposed into some combination of axial tension, bending, torsion, and compression Almost always, one mode dominates So common is this that the functional

name given to the component describes the way it is loaded:tiescarry tensile

loads; beams carry bending moments; shafts carry torques; and columns

carry compressive axial loads The words ‘‘tie’’, ‘‘beam’’, ‘‘shaft’’, and ‘‘col-umn’’ each imply a function Many simple engineering functions can be described by single words or short phrases, saving the need to explain the function in detail Here we explore property limits and material indices for some of these

Material index for a light, strong tie-rod A design calls for a cylindrical tie-rod of specified lengthLto carry a tensile forceFwithout failure; it is to be of

minimum mass, as in the uppermost sketch in Figure 5.7 The length L is

specified but the cross-section areaAis not Here, ‘‘maximizing performance’’

means ‘‘minimizing the mass while still carrying the loadFsafely’’ The design

requirements, translated, are listed in Table 5.4

We first seek an equation describing the quantity to be maximized or

minimized Here it is the massmof the tie, and it is a minimum that we seek

This equation, calledthe objective function, is

mẳAL 5:1ị

where Ais the area of the cross-section and is the density of the material

of which it is made The length L and force F are specified and are

there-fore fixed; the cross-sectionA, is free We can reduce the mass by reducing the

cross-section, but there is a constraint: the section-areaAmust be sufficient to

Table 5.3 Function, constraints, objective, and free variables for the transmission line

Function Long span transmission line

Constraints SpanLis specified

Material must be strengthf>80 MPa

Objective Minimize electrical resistivitye

(101)

carry the tensile loadF, requiring that

F

A f ð5:2Þ

wherefis the failure strength EliminatingAbetween these two equations give

m ðFÞðLÞ

f

ð5:3Þ

Note the form of this result The first bracket contains the specified loadF The

second bracket contains the specified geometry (the length Lof the tie) The

last bracket contains the material properties The lightest tie that will carryF

L

F F

T

F F

F

Area A,

Area A, second moment of

area Ιxx

Area A, second moment of

area Ιxx Area A, polar moment of

area J

(b) Bending: beam

(c) Torsion: shaft

(d) Compression: column (a) Tension: tie

Figure 5.7 A cylindrical tie-rod loaded (a) in tension, (b) in bending, (c) in torsion and (d) axially, as a column The best choice of materials depends on the mode of loading and on the design goal; it is found by deriving the appropriate material index

Table 5.4 Design requirements for the light tie

Function Tie rod

Constraints LengthLis specified

Tie must support axial tensile loadFwithout failing

Objective Minimize the mass m of the tie

Free variables Cross-section area,A

Choice of material

(102)

safely2is that made of the material with the smallest value of/

f We could

define this as the material index of the problem, seeking a minimum, but it is more usual, when dealing with specific properties, to express them in a form for which a maximum is sought We therefore invert the material properties in

equation (5.3) and define the material indexM, as

Mẳf

5:4ị

The lightest tie-rod that will safely carry the loadFwithout failing is that with

the largest value of this index, the ‘‘specific strength’’, plotted in the chart of Figure 4.6 A similar calculation for a lightstifftie (one for which the stiffnessS

rather than the strengthfis specified) leads to the index

MẳE

5:5ị

whereEis Youngs modulus This time the index is the ‘‘specific stiffness’’, also

shown in Figure 4.6 The material group (rather than just a single property)

appears as the index in both cases because minimizing the mass m— the

objective — was coupled to one of the constraints, that of carrying the loadF

without failing or deflecting too much

That was easy Now for a slightly more difficult (and important) one

Material index for a light, stiff beam The mode of loading that most com-monly dominates in engineering is not tension, but bending — think of floor joists, of wing spars, of golf-club shafts Consider, then, a light beam of square

section bb and length L loaded in bending It must meet a constraint on

its stiffness S, meaning that it must not deflect more than under a load F

(Figure 5.8) Table 5.5 translates the design requirements

Appendix A of this book catalogues useful solutions to a range of standard problems The stiffness of beams is one of these Turning to Section A3 we find

an equation for the stiffnessSof an elastic beam The constraint requires that

S¼F/ be greater than this:

SẳFC1EI

L3 5:6ị

whereEis Youngs modulus,C1is a constant that depends on the distribution

of load andIis the second moment of the area of the section, which, for a beam

of square section (‘‘Useful Solutions’’, Appendix A, Section A.2), is

I¼b

4

12ẳ

A2

12 5:7ị

2 In reality a safety factor,Sf, is always included in such a calculation, such that equation (5.2) becomes

(103)

The stiffnessSand the lengthLare specified; the section areaAis free We can

reduce the mass of the beam by reducing A, but only so far that the stiffness

constraint is still met Using these two equations to eliminate Ain equation

(5.1) for the mass gives

m 12S

C1L 1=2

ðL3Þ

E1=2

ð5:8Þ

The brackets are ordered as before: functional requirement, geometry and material The best materials for a light, stiff beam are those with the smallest values of/E1/2 As before, we will invert this, seeking instead large values of the material index

MẳE

1=2

5:9ị

In deriving the index, we have assumed that the section of the beam

remained square so that both edges changed in length whenAchanged If one

of the two dimensions is held fixed, the index changes A panel is a flat plate

with a given lengthLand widthW; the only free variable (apart from material)

is the thicknesst For this the index becomes (via an identical derivation)

M¼E

1=3

ð5:10Þ

L Square section

area A = b2

b

Force F

b

δ

Figure 5.8 A beam of square section, loaded in bending Its stiffness isS¼F/ whereFis the load and is the deflection

Table 5.5 Design requirements for the light stiff beam

Function Beam

Constraints LengthLis specified

Beam must support a bending loadFwithout deflecting too much, meaning that the bending stiffnessSis specified

Objective Minimize the mass of the beam

Free variables Cross-section area,A

Choice of material

(104)

Note the procedure The length of the rod or beam is specified but we are free

to choose the section areaA The objective is to minimize its mass,m We write

an equation form:it is the objective function But there is a constraint: the rod

must carry the loadFwithout yielding in tension (in the first example) or bending

too much (in the second) Use this to eliminate the free variableAand read off the

combination of properties,M, to be maximized It sounds easy, and it is so long

as you are clear from the start what the constraints are, what you are trying to maximize or minimize, which parameters are specified and which are free

Deriving indices — how to it

This is a good moment to describe the method in more general terms.Structural

elements are components that perform a physical function: they carry loads,

transmit heat, store energy, and so on: in short, they satisfyfunctional

require-ments The functional requirements are specified by the design: a tie must carry a specified tensile load; a spring must provide a given restoring force or store a given energy, a heat exchanger must transmit heat a given heat flux, and so on The performance of a structural element is determined by three things: the functional requirements, the geometry and the properties of the material of

which it is made.3 The performance P of the element is described by an

equation of the form

P¼ Functional

requirements,F

, Geometric

parameters,G

, Material

properties,M

or

PẳfF;G;Mị 5:11ị

whereP, theperformance metric, describes some aspect of the performance of

the component: its mass, or volume, or cost, or life for example; and ‘‘f’’ means

‘‘a function of’’.Optimum designis the selection of the material and geometry

that maximize or minimizeP, according to its desirability or otherwise

The three groups of parameters in equation (5.11) are said to beseparable

when the equation can be written

Pẳf1Fị f2ðGÞ f3ðMÞ ð5:12Þ

wheref1,f2, andf3are separate functions that are simply multiplied together

When the groups are separable, as they frequently are, the optimum choice of material becomes independent of the details of the design; it is the same for all

geometries, G, and for all values of the function requirement, F Then the

optimum subset of materials can be identified without solving the complete

design problem, or even knowing all the details of F and G This enables

(105)

enormous simplification: the performance for all F and G is maximized by

maximizing f3(M), which is called the material efficiency coefficient, or

material index for short The remaining bit, f1(F)f2(G), is related to the structural efficiency coefficient, orstructural index We not need it now, but will examine it briefly in Section 5.7

Each combination of function, objective and constraint leads to a material index (Figure 5.9); the index is characteristic of the combination, and thus of the function the component performs The method is general, and, in later chapters, is applied to a wide range of problems Table 5.6 gives examples of indices and the design problems that they characterize A fuller catalogue of indices is given in Appendix B New problems throw up new indices, as the case studies of the next chapter will show

5.4 The selection procedure

We can now assemble the four steps into a systematic procedure

Translation

Table 5.7 says it all Simplified: identify the material attributes that are constrained by the design, decide what you will use as a criterion of excellence (to be minimized or maximized), substitute for any free variables using one of the constraints, and read off the combination of material properties that optimize the criterion of excellence

Functions Tie

Beam

Shaft

Column

Mechanical, thermal electrical

Constraints Stiffness specified

Failure load specified

Fatigue life specified

Geometry specified

Minimize this (or maximize reciprocal) Minimize cost

Minimize mass

Maximize energy storage Minimize environmental impact

Objectives

Index

M =ρ/E1/2

Figure 5.9 The specification of function, objective, and constraint leads to a materials index The combination in the highlighted boxes leads to the indexE1/2/

(106)

Screening: applying attribute limits

Any design imposes certain non-negotiable demands (‘‘constraints’’) on the material of which it is made We have explained how these are translated into attribute limits Attribute limits plot as horizontal or vertical lines on material

selection charts, illustrated in Figure 5.10 It shows a schematicEchart, in

the manner of Chapter We suppose that the design imposes limits on these of

E>10 GPa and <3 Mg/m3, shown on the figure The optimizing search is

restricted to the window boxed by the limits, labeled ‘‘Search region’’ Less quantifiable properties such as corrosion resistance, wear resistance or form-ability can all appear as primary limits, which take the form

A>A

or

A<A ð5:13Þ

Table 5.6 Examples of material-indices

Function, objective, and constraints Index

Tie, minimum weight, stiffness prescribed E

Beam, minimum weight, stiffness prescribed E

1=2

Beam, minimum weight, strength prescribed

2=3

y

Beam, minimum cost, stiffness prescribed E

1=2

Cm

Beam, minimum cost, strength prescribed

2=3

y Cm

Column, minimum cost, buckling load prescribed E

1=2

Cm

Spring, minimum weight for given energy storage

2 y E

Thermal Insulation, minimum cost, heat flux prescribed

lCp

Electromagnet, maximum field, temperature rise prescribed Cp

e

¼density;E¼Young’s modulus;y¼elastic limit;Cm¼cost/kg¼thermal conductivity;e¼electrical

(107)

Modulus E = 10 GPa

Metals

Elastomers

Ceramics

Woods

Foams

0.1 10

1 100

0.01 1000

100

0.1 10

Density (Mg/m3)

Y

o

u

n

g

’s

mo

d

u

lu

s

E

(G

Pa

)

Modulus-Density

MFA, 04

Polymers Compposites

Density ρ = Mg/m3 Search

region

s P

Figure 5.10 A schematicEchart showing a lower limit forEand an upper one for Table 5.7 Translation

Step Action

1 Define the design requirements:

(a) Function: what does the component do?

(b) Constraints: essential requirements that must be met: stiffness, strength, corrosion resistance, forming characteristics,

(c) Objective: what is to be maximized or minimized?

(d) Free variables: what are the unconstrained variables of the problem?

2 List the constraints (no yield; no fracture; no buckling, etc.) and develop an equation for them if necessary

3 Develop an equation for the objective in terms of the functional requirements, the geometry and the material properties (the objective function)

4 Identify the free (unspecified) variables

5 Substitute for the free variables from the constraint equations into the objective function

6 Group the variables into three groups: functional requirements,F, geometry,G, and material properties,M, thus

Performance metricP f1ðFÞ f2ðGÞ f3ðMÞ

or

Performance metricPf1ðFÞ f2ðGÞ f3ðMÞ

7 Read off the material index, expressed as a quantityM, that optimizes the performance metricP.Mis the criterion of excellence

(108)

whereAis an attribute (service temperature, for instance) andA*is a critical value of that attribute, set by the design, that must be exceeded, or (in the case

of corrosion rate) mustnot be exceeded

One should not be too hasty in applying attribute limits; it may be possible to engineer a route around them A component that gets too hot can be cooled; one that corrodes can be coated with a protective film Many designers apply attribute

limits for fracture toughness,K1Cand ductilityEfinsisting on materials with,

as rules of thumb, K1C>15MPa:m1=2andEf >2% in order to guarantee

adequate tolerance to stress concentrations By doing this they eliminate ma-terials that the more innovative designer is able to use to good purpose (the limits just cited forK1CandEfeliminate all polymers and all ceramics, a rash step too

early in the design) At this stage, keep as many options open as possible

Ranking: indices on charts

The next step is to seek, from the subset of materials that meet the property limits, those that maximize the performance of the component We will use the design of light, stiff components as an example; the other material indices are used in a similar way

Figure 5.11 shows, as before, modulusE, plotted against density , on log

scales The material indices E/, E1/2/, and E1/3/ can be plotted onto the

figure The condition

E

¼C

or, taking logs,

LogđEỡ ỬLogđỡ ợLogđCỡ đ5:14ỡ

is a family of straight parallel lines of slope on a plot of Log(E) against Log()

each line corresponds to a value of the constantC The condition

E1=2

ẳC 5:15ị

or, taking logs again,

LogđEỡ Ử2Logđỡ ợ2LogđCỡ đ5:16ỡ

gives another set, this time with a slope of 2; and

E1=3

ẳC 5:17ị

gives yet another set, with slope We shall refer to these lines asselection

(109)

It is now easy to read off the subset materials that optimally maximize performance for each loading geometry All the materials that lie on a line of

constantE1/2/perform equally well as a light, stiff beam; those above the line

are better, those below, worse Figure 5.12 shows a grid of lines corresponding

to values ofE1/2/from 0.1 to in units of GPa1/2/(Mg/m3) A material with

M¼1 in these units gives a beam that has one tenth the weight of one with

M¼0.1 The subset of materials with particularly good values of the index is

identified by picking a line that isolates a search area containing a reasonably small number of candidates, as shown schematically in Figure 5.13 as a diagonal selection line Attribute limits can be added, narrowing the search

window: that corresponding to E>50 GPa is shown as a horizontal line

The short-list of candidate materials is expanded or contracted by moving the index line

We now have a ranked short-list of potential candidate materials The last step is to explore their character in depth The list of constraints usually contains

Metals

Elastomers

Ceramics

Woods

Foams

0.1 10

1 100

0.01 1000

100

0.1 10

Density (Mg/m3)

Y

o

u

n

g

’s

mo

d

u

lu

s

E

(

G

Pa

)

Modulus-Density

MFA, 04 Polymers

Compposites

E1/22///ρ

E1/33///ρ E///ρ

Guidelines for minimum mass

design

1

2 33

Figure 5.11 A schematicEchart showing guidelines for the three material indices for stiff, lightweight design

(110)

Metals

Elastomers Ceramics

Woods

Foams

0.1 10

1 100

0.01 1000

100

0.1 10

Density (Mg/m3)

Y

o

u

n

g

’s

mo

d

u

lu

s

E (GPa)

Modulus-Density

E1/22///ρ (GPa)1/22/(Mg/m33)

0.1 0.3

3

MFA, 04

Increasing values of index E1/22///ρ

Polymers Comppositess

Search region

Figure 5.12 A schematicEchart showing a grid of lines for the material indexM¼E1/2/ The units

are (GPa)1/2/(Mg/m3)

Metals

Elastomers Ceramics

Woods

Foams 0.1

10

1 100

0.01 1000

100

0.1 10

Density (Mg/m3)

Y

o

u

n

g

’s

mo

d

u

lu

s

E (GPa)

Modulus-Density

MFA, 04

Polymers Comppositess

Search region

Index E1/22/// = 3ρ

Modulus E = 50 GPa

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some that cannot be expressed as simple attribute limits Many of these relate to the behavior of the material in a given environment, or when in contact with another material, or to aspects of the ways in which the material can be shaped, joined, or finished Such information can be found in handbooks, manufacturers data-sheets, or on the internet And then — it is to be antici-pated — there are the constraints that have been overlooked simply because they were not seen as such Confidence is built by seeking design guidelines, case studies or failure analyses that document each candidate, building a dossier of its strengths, its weaknesses, and ways in which these can be over-come All of these come under the heading of supporting information Finding it is the subject of Chapter 15

The selection procedure is extended in Chapters and 11 to deal with multiple constraints and objectives and to include section shape Before moving on to these, it is a good idea to consolidate the ideas so far by applying them to a number of case studies They follow in Chapter

5.5 Computer-aided selection

The charts of Chapter give an overview, but the number of materials that can be shown on any one of them is obviously limited Selection using them is practical when there are very few constraints, as the examples of Section 5.3 showed, but when there are many — as there usually are — checking that a given material meets them all is cumbersome Both problems are overcome by computer implementation of the method

The CES material and process selection software4is an example of such an

implementation A database contains records for materials, organized in the hierarchical manner shown in Figure 5.2 Each record contains structured property-data for a material, each stored as a range spanning the typical (or, often, the permitted) range of values of that property It also contains limited unstructured data in the form of text, images, and references to sources of information about the material The data are interrogated by a search engine that offers search interfaces shown schematically in Figure 5.14 On the left is a simple query interface for screening on single properties The desired upper or lower limits for constrained attributes are entered; the search engine rejects all materials with attributes that lie outside the limits In the center is shown a second way of interrogating the data: a bar chart like that shown earlier as Figure 4.1 It and the bubble chart shown on the right are the ways both of applying constraints and of ranking Used for ranking, a selection line or box is super-imposed on the charts with edges that lie at the constrained values of the property (bar chart) or properties (bubble chart), eliminating the material in the shaded areas, and leaving the materials that

4

Granta Design Ltd., Cambridge, UK (www.grantadesign.com)

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meet all the constraints If instead, ranking is sought (having already applied all necessary constraints) the line or box is positioned so that a few — say, three — materials are left in the selected area; these are the top ranked candidates

The figure illustrates an elaboration of the heat sink example given earlier, in which we now add more constraints (Table 5.8) The require-ments are as before, plus the requirement that the modulus be greater

than 50 GPa, that the expansion coefficient, lies between and 10106/

C and that the maximum service temperature exceeds 120C All are

applied as property limits on the left-hand window, implementing a screening stage

Ranking on thermal conductivity is shown in the central window Materials that fail the screening stage on the left are grayed-out; those that pass remain colored The selection line has been positioned so that two classes of material lie in the search region The top-ranked candidate is aluminum nitride, the second is alumina If, for some reason, the mass of the heat sink was also important, it might instead be desired to rank using

material index /, where is the density Then the window on the right,

showing a chart, allows selection by /, plotted as diagonal contour

on the schematic The materials furthest above the line are the best choice Once again, AlN wins

All materials

Selected materials Density kg/m3

Price $/kg

Modulus GPa

Strength MPa

Max service T C T-expansion 10-6/C

Resistivity µΩ.cm General properties Min Max

Mechanical properties Thermal properties Electrical properties 1019 2 10 120 50 0.01 1000 T her m a l C onduc ti v it y ( W /m K

) Aluminum nitride

Alumina Silica glass Borosilicate glass Search region Selection line Aluminum nitride Alumina Silica glass Borosilicate glass Search region Selection line Contour of λ/ρ

0.01 1000 T h er m a l C onduc ti v it y ( W /m K )

Density (Mg/m3)

0.01 50

Foams Polymers

Ceramcs Metals

Figure 5.14 Computer-aided selection using the CES software The schematic shows the three types of selection window They can be used in any order and any combination The

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The software contains not one, but two databases The first of these contains the 68 material classes shown in the charts of Chapter — indeed all these charts were made using the software They are chosen because they are those most widely used; between them they account for 98 percent of material usage This database allows a first look at a problem, but it is inadequate for a fuller exploration The second database is much larger — it contains data for over 3000 materials By changing the database, the selection criteria already entered

are applied instead to the much larger population Doing this (and ranking on

as in the central window) gives the top rank candidates listed in Table 5.9,

listed in order of decreasing Diamond is outstanding but is probably

impracticable for reasons of cost; and compounds of beryllium (beryllia is beryllium oxide) are toxic and for this reason perhaps undesirable That leaves us with aluminum nitride, our earlier choice Part of a record for one grade of aluminum nitride is shown in Table 5.10 The upper part lists structured data (there is more, but it’s not relevant in this example) The lower part gives the limited unstructured data provided by the record itself, and references to sources that are linked to the record in which more supporting information can be found The search engine has a further feature, represented by the button labeled ‘‘search web’’ next to the material name at the top Activating it sends the material name as a string to a web search engine, delivering supporting information available there

Examples of the use of the software appear later in the book

Table 5.8 Function, expanded constraints, objective, and free variable for the heat sink

Function Heat sink

Constraints Material must be ‘‘good insulator’’, ore>1019m.cm ModulusE>50 GPa

Maximum service temperature Tmax>120C Expansion coefficient 2106< <10106/C

All dimensions are specified

Objective Maximize thermal conductivity,or conductivity per unit mass/

Free variables Choice of material

Table 5.9 The selection Material

Diamond

Beryllia (Grade 99) Beryllia (Grade B995) Beryllia (Grade BZ)

Aluminum nitride (fully dense) Aluminum nitride (97 percent dense)

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5.6 The structural index

Books on optimal design of structures (e.g Shanley, 1960) make the point that the efficiency of material usage in mechanically loaded components depends on the product of three factors: the material index, as defined here; a factor describing section shape, the subject of our Chapter 11; and a

structural index,5which contains elements of theGandFof equation (5.12). Table 5.10 Part of a record for aluminum nitride, showing structured and unstructured data,

references and the web-search facility

Aluminum Nitride

General properties

Density 3.26–3.33 Mg/m3 Price *70–95 $/kg

Mechanical properties

Young’s M modulus 302–348 GPa Hardness — Vickers 990–1260 HV Compressive strength 1970–2700 MPa Fracture toughness 2.5–3.4 MPa.m1/2

Design guidelines Aluminum nitride (AlN) has an unusual combination of properties: it is an electrical insulator, but an excellent conductor of heat This is just what is wanted for substrates for high-powered electronics; the substrate must insulate yet conduct the heat out of the microchips This, and its high strength, chemical stability, and low expansion give it a special role as a heat sinks for power electronics

Aluminum nitride starts as a powder, is pressed (with a polymer binder) to the desired shape, then fired at a high temperature, burning off the binder and causing the powder to sinter

Technical notes Aluminum nitride is particularly unusual for its high thermal conductivity combined with a high electrical resistance, low dielectric constant, good corrosion, and thermal shock resistance

Typical uses Substrates for microcircuits, chip carriers, heat sinks, electronic components; windows, heaters, chucks, clamp rings, gas distribution plates

References

Handbook of Ceramics, Glasses and Diamonds, (2001) Harper, C.A editor, McGraw-Hill, New York, NY, USA ISBN 0-07-026712-X.(A comprehensive compilation of data and design guidelines.)

Handbook of structural ceramics, editor: M.M Schwartz, McGraw-Hill, New York, USA (1992)

Morrell, R.Handbook of properties of technical & engineering ceramics, Parts I and II, National Physical Laboratory, Her Majesty’s Stationery Office, London, UK (1985)

Thermal properties

Thermal conductivity 80–200 W/m.K Thermal expansion 4.9–6.2mstrain/K Max service

temperature

*1027–1727C

Electrical properties

Resistivity 1e18–1e21m.cm

Dielectric constant 8.3–9.3

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The subjects of this book — material and process selection — focuses on the material index and on shape; but we should examine the structural index briefly, partly to make the connection with the classical theory of optimal design, and partly because it becomes useful (even to us) when structures are scaled in size

In design for minimum mass (equations (5.3) and (5.8)), a measure of the

efficiency of the design is given by the quantity m/L3 Equation (5.3), for

instance, can be written

m L3

F L2

f

ð5:18Þ

and equation (5.8) becomes

m L3

12

C1 1=2

S L

1=2

E1=2

ð5:19Þ

This m/L3 has the dimensions of density; the lower this pseudo-density the

lighter is the structure for a given scale, and thus the greater is the structural efficiency The first bracketed term on the right of the equation is merely a

constant The last is the material index The middle one, F/L2 for

strength-limited design andS/Lfor stiffness limited design, is called thestructural index It has the dimensions of stress; it is a measure of the intensity of loading Design proportions that are optimal, minimizing material usage, are optimal for structures of any size provided they all have the same structural index The performance equation (5.8), was written in a way that isolated the structural index, a convention we shall follow in the case studies of Chapter

The structural index for a component of minimum cost is the same as that

for one of minimum mass; it isF/L2again for strength limited design,S/Lwhen

it is stiffness For beams or columns of minimum mass, cost, or energy content,

they is the same For panels (dimensionsLW) loaded in bending or such that

they buckle it isFW/L3andSW2/L3whereLandWare the (fixed) dimensions

of the panel

Material selection is tacked in four steps

Translation— reinterpreting the design requirements in terms of function, constraints, objectives, and free variables

Screening— deriving attribute limits from the constraints and applying these to isolate a subset of viable materials

Ranking— ordering the viable candidates by the value of a material index, the criterion of excellence that maximizes or minimizes some measure of performance

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Seeking supporting information for the top-ranked candidates, exploring aspects of their past history, their established uses, their behavior in relevant environments, their availability and more until a sufficiently detailed picture is built up that a final choice can be made

Hard-copy material charts allow a first go at the task, and have the merit of maintaining breadth of vision: all material classes are in the frame, so to speak But materials have many properties, and the number of combinations of these appearing in indices is very much larger It is impractical to print charts for all of them Even if you did, their resolution is limited Both problems are over-come by computer implementation, allowing freedom to explore the whole kingdom of materials and also providing detail when required

5.8 Further reading

The books listed below discuss optimization methods and their application in materials engineering None contain the approach developed here

Dieter, G.E (1991) Engineering Design, a Materials and Processing Approach, 2nd

edition, McGraw-Hill, New York, USA ISBN 0-07-100829-2.(A well-balanced and

respected text focusing on the place of materials and processing in technical design.)

Gordon, J.E (1976) The New Science of Strong Materials, or why you don’t Fall

Through the Floor, 2nd edition, Penguin Books, Harmondsworth, UK ISBN

0-1402-0920-7 (This very readable book presents ideas about plasticity and fracture, and

ways of designing materials to prevent them.)

Gordon, J.E (1978) Structures, or why Things don’t Fall Down, Penguin Books,

Harmondsworth, UK ISBN 0-1402-1961-7 (A companion to the other book by

Gordon (above), this time introducing structural design.)

Shanley, F.R (1960) Weight-Strength Analysis of Aircraft Structures, 2nd edition,

Dover Publications, Inc New York, USA Library of Congress Number 60-50107.(A

remarkable text, no longer in print, on the design of light-weight structures.)

Arora, J.S (1989)Introduction to Optimum Design, McGraw-Hill, New York, USA

ISBN 0-07-002460-X.(An introduction to the terminology and methods of

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t R ω

L b

t

W

Temp Ti

2r t

Chapter contents

6.1 Introduction and synopsis 106 6.2 Materials for oars 106 6.3 Mirrors for large telescopes 110 6.4 Materials for table legs 114 6.5 Cost: structural materials

for buildings 117 6.6 Materials for flywheels 121 6.7 Materials for springs 126 6.8 Elastic hinges and couplings 130 6.9 Materials for seals 133 6.10 Deflection-limited design with

brittle polymers 136 6.11 Safe pressure vessels 140

6.12 Stiff, high damping materials for

shaker tables 144 6.13 Insulation for short-term

isothermal containers 147 6.14 Energy-efficient kiln walls 151 6.15 Materials for passive solar heating 154 6.16 Materials to minimize thermal

distortion in precision devices 157 6.17 Nylon bearings for ships’ rudders 160 6.18 Materials for heat exchangers 163 6.19 Materials for radomes 168 6.20 Summary and conclusions 172 6.21 Further reading 172

Chapter 6

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Here we have a collection of case studies illustrating the screening methods of Chapter They are deliberately simplified to avoid obscuring the method under layers of detail In most cases little is lost by this: the best choice of material for the simple example is the same as that for the more complex, for the reasons given in Chapter More realistic case studies are developed in later chapters

Each case study is laid out in the same way:

(a) the problem statement, setting the scene,

(b) the model, identifying function, constraints, objectives, and free variables, from which emerge the attribute limits and material indices,

(c) the selectionin which the full menu of materials is reduced by screening and ranking to a short-list of viable candidates,

(d) the postscript, allowing a commentary on results and philosophy Techniques for seeking supporting information are left to later chapters

The first few examples are simple but illustrate the method well Later examples are less obvious and require clear thinking to identify and distinguish objectives and constraints Confusion here can lead to bizarre and misleading conclusions Always apply common sense: does the selection include the tra-ditional materials used for that application? Are some members of the subset obviously unsuitable? If they are, it is usually because a constraint has been overlooked: it must be formulated and applied

Most of the case studies use the hard-copy charts of Chapter 4; Sections 6.17 and 6.18 illustrate the use of computer-based selection, using the same methodology

6.2 Materials for oars

Credit for inventing the rowed boat seems to belong to the Egyptians Boats with oars appear in carved relief on monuments built in Egypt between 3300 and 3000 BC Boats, before steam power, could be propelled by poling, by sail, or by oar Oars gave more control than the other two, the military potential of which was well understood by the Romans, the Vikings and the Venetians

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people and goods across the river Gradually gentlemen became involved (notably the young gentlemen of Oxford and Cambridge), sophisticating both the rules and the equipment The real stimulus for development of boat and oar came in 1900 with the establishment of rowing as an Olympic sport Since then both have drawn to the full on the craftsmanship and materials of their day Consider, as an example, the oar

The model Mechanically speaking, an oar is a beam, loaded in bending It must be strong enough to carry, without breaking, the bending moment exerted by the oarsman, it must have a stiffness to match the rower’s own characteristics and give the right ‘‘feel’’, and — very important — it must be as light as possible Meeting the strength constraint is easy Oars are designed on

stiffness, that is, to give a specified elastic deflection under a given load The upper part of Figure 6.1 shows an oar: a blade or ‘‘spoon’’ is bonded to a shaft or ‘‘loom’’ that carries a sleeve and collar to give positive location in the rowlock The lower part of the figure shows how the oar stiffness is measured: a 10-kg weight is on the oar 2.05 m from the collar and the deflection at this point is measured A soft oar will deflect nearly 50 mm; a hard one only 30 A rower, ordering an oar, will specify how hard it should be

The oar must also be light; extra weight increases the wetted area of the hull and the drag that goes with it So there we have it: an oar is a beam of specified stiffness and minimum weight The material index we want was derived in Chapter as equation (5.9) It is that for a light, stiff beam:

M¼E

1=2

ð6:1Þ

where E is Young’s modulus and is the density There are other obvious constraints Oars are dropped, and blades sometimes clash The material must be tough enough to survive this, so brittle materials (those with a toughnessG1C

Handle Collar Sleeve Spoon

Loom

δ

Figure 6.1 An oar Oars are designed on stiffness, measured in the way shown in the lower figure, and they must be light

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less than kJ/m2) are unacceptable Given these requirements, summarized in Table 6.1, what materials would you choose to make oars?

The selection Figure 6.2 shows the appropriate chart: that in which Young’s modulus,E, is plotted against density, The selection line for the indexMhas a slope of 2, as explained in Section 5.4; it is positioned so that a small group of materials is left above it They are the materials with the largest values ofM, and it is these that are the best choice, provided they satisfy the other constraint Table 6.1 Design requirements for the oar

Function Oar — meaning light, stiff beam

Constraints LengthLspecified

Bending stiffnessSspecified ToughnessG1C>1 kJ/m2

Objective Minimize the mass

Free variables Shaft diameter Choice of material

E1/3 ρ E1/2 ρ E ρ

104m/s

103m/s

102m/s Longitudinal wave speed Guidelines for minimum mass design D

0 0011

Y oo uu nn gg ''sm o s mo dd uu lluu sEs, E (( GG P a )

100-44

0.1 10

10-3 10-2 10-1 10 100 1000 Polyesterolyest P y Foams Polymers and elastomersy Metals Technical ceramics Composites Natural materials Lead alloys W alloyslloys Steels Ti alloys Mg alloys M o CFRP C GFRP Al alloys A mer mer Rigid polym foams Flexible polymer foams

Ni alloysalloys

Cu alloysy

Zinc alloysalloys PA PEEK PMMA PC PETT Cork Wood Butyl rubber Silicone elastomers e Concretee WC WC Al2O3

B4C

Epoxies PS PTFE EVA Neoprene Isoprene Polyurethane Leatherher L L MFA, 04 PP PE PE

Glassassss Glass s els oys N s eels loys A els oys Search region

E1/22///ρ

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(a simple attribute-limits on toughness) They contain three classes of material: woods, carbon reinforced polymers, and certain ceramics (Table 6.2) Ceramics are brittle; the toughness-modulus chart of Figure 4.7 shows that all fail to meet that required by the design The recommendation is clear Make your oars out of wood or — better — out of CFRP

Postscript Now we know what oars should be made of What, in reality, is used? Racing oars and sculls are made either of wood or of a high performance composite: carbon-fiber reinforced epoxy

Wooden oars are made today, as they were 100 years ago, by craftsmen working largely by hand The shaft and blade are of Sitka spruce from the northern US or Canada, the further north the better because the short growing season gives a finer grain The wood is cut into strips, four of which are laminated together to average the stiffness and the blade is glued to the shaft The rough oar is then shelved for some weeks to settle down, and finished by hand cutting and polishing The final spruce oar weighs between and 4.3 kg, and costs (in 2004) about $250

Composite blades are a little lighter than wood for the same stiffness The component parts are fabricated from a mixture of carbon and glass fibers in an epoxy matrix, assembled and glued The advantage of composites lies partly in the saving of weight (typical weight: 3.9 kg) and partly in the greater control of performance: the shaft is molded to give the stiffness specified by the purchaser Until recently a CFRP oar cost more than a wooden one, but the price of carbon fibers has fallen sufficiently that the two cost about the same

Could we better? The chart shows that wood and CFRP offer the lightest oars, at least when normal construction methods are used Novel composites, not at present shown on the chart, might permit further weight saving; and functional-grading (a thin, very stiff outer shell with a low density core) might it But both appear, at present, unlikely

Further reading Redgrave, S (1992)Complete Book of Rowing, Partridge Press, London Related case

studies

6.3 Mirrors for large telescopes 6.4 Table legs

12.2 Spars for man-powered planes 12.4 Forks for a racing bicycle Table 6.2 Material for oars

Material Index M(GPa)1/2/(Mg/m3) Comment

Woods 3.4 –6.3 Cheap, traditional, but with natural variability CFRP 5.3 –7.9 As good as wood, more control of properties Ceramics –8.9 GoodMbut toughness low and cost high

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6.3 Mirrors for large telescopes

There are some very large optical telescopes in the world The newer ones employ complex and cunning tricks to maintain their precision as they track across the sky — more on that in the postscript But if you want a simple tele-scope, you make the reflector as a single rigid mirror The largest such telescope is sited on Mount Semivodrike, near Zelenchukskaya in the Caucasus Mountains of Russia The mirror is m (236 in.) in diameter To be sufficiently rigid, the mirror, which is made of glass, is about m thick and weighs 70 tonnes

The total cost of a large (236 in.) telescope is, like the telescope itself, astro-nomical — about US$280 m The mirror itself accounts for only about percent of this cost; the rest is that of the mechanism that holds, positions, and moves it as it tracks across the sky This mechanism must be stiff enough to position the mirror relative to the collecting system with a precision about equal to that of the wavelength of light It might seem, at first sight, that doubling the massmof the mirror would require that the sections of the support-structure be doubled too, so as to keep the stresses (and hence the strains and displacements) the same; but the heavier structure then deflects under its own weight In practice, the sections have to increase as m2, and so does the cost

Before the turn of the century, mirrors were made of speculum metal (den-sity: about Mg/m3) Since then, they have been made of glass (density: 2.3 Mg/m3), silvered on the front surface, so none of the optical properties of the glass are used Glass is chosen for its mechanical properties only; the 70 tonnes of glass is just a very elaborate support for 100 nm (about 30 g) of silver Could one, by taking a radically new look at materials for mirrors, suggest possible routes to the construction of lighter, cheaper telescopes?

The model At its simplest, the mirror is a circular disk, of diameter 2Rand mean thicknesst, simply supported at its periphery (Figure 6.3) When hori-zontal, it will deflect under its own weightm; when vertical it will not deflect significantly This distortion (which changes the focal length and introduces aberrations) must be small enough that it does not interfere with performance; in practice, this means that the deflection of the midpoint of the mirror must be less than the wavelength of light Additional requirements are: high-dimensional stability (no creep), and low thermal expansion (Table 6.3)

The mass of the mirror (the property we wish to minimize) is

mẳR2t 6:2ị

whereis the density of the material of the disk The elastic deflection, , of the center of a horizontal disk due to its own weight is given, for a material with Poisson’s ratio of 0.3 (Appendix A), by

¼

4 mgR2

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The quantitygin this equation is the acceleration due to gravity: 9.81 m/s2;E, as before, is Young’s modulus We require that this deflection be less than (say) 10mm The diameter 2Rof the disk is specified by the telescope design, but the thickness tis a free variable Solving for tand substituting this into the first equation gives

m¼ 3g

4 1=2

R4

E1=3

h i3=2

ð6:4Þ

The lightest mirror is the one with the greatest value of the material index

M¼E

1=3

ð6:5Þ

We treat the remaining constraints as attribute limits, requiring a melting point greater than 500C to avoid creep, zero moisture take up, and a low thermal expansion coefficient ( <20106/K)

t

2R Concave support

for reflecting surface

δ

Figure 6.3 The mirror of a large optical telescope is modeled as a disk, simply supported at its periphery It must not sag by more than a wavelength of light at its center

Table 6.3 Design requirements for the telescope mirror Function Precision mirror

Constraints RadiusRspecified

Must not distort more than under self-weight

High dimensional stability: no creep, low thermal expansion

Objective Minimize the mass,m

Free variables Thickness of mirror,t

Choice of material

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The selection Here we have another example of elastic design for minimum weight The appropriate chart is again that relating Young’s modulus Eand density— but the line we now construct on it has a slope of 3, corresponding to the condition M¼E1/3/¼constant (Figure 6.4) Glass lies at the value

M¼1.7 (GPa)1/3.m3/Mg Materials that have larger values of M are better, those with lower, worse Glass is much better than steel or speculum metal (that is why most mirrors are made of glass), but it is less good than magne-sium, several ceramics, carbon–fiber, and glass–fiber reinforced polymers, or — an unexpected finding — stiff foamed polymers The short-list before applying the attribute limits is given in Table 6.4

One must, of course, examine other aspects of this choice The mass of the mirror, calculated from equation (6.4), is listed in the table The CFRP mirror is less than half the weight of the glass one, and that the support-structure could thus be as much as times less expensive The possible saving by using foam is even greater But could they be made?

E1/3 ρ E1/2 ρ E ρ

104m/s

103 m/s

102m/s Longitudinal wave speed Guidelines for minimum mass design D

Deennsisitty, y,ρρ ((MMgg//mm3)

0 0011

Y oo uu nn gg ''sm o s mo dd uu lluu sEs , E (( GG P a )

100-44

0.1 10

10-3 10-2 10-1 10 100 1000

Polyesterolyesty

Foams Polymers and elastomersy Metals Technical ceramics Composites Natural materials Lead alloys W alloyslloys Steels Ti alloys Mg alloys M o CFRP C GFRP Al alloys A mer mer Rigid polym foams Flexible polymer foams

Ni alloysalloys

Cu alloysy

Zinc alloysalloys PA PEEK PMMA PC PETT Cork Wood Butyl rubber Silicone elastomers Concretee WC WC Al2O3

SiC Si Si33NN44

Young's modulus - Density

B4C

Epoxies PS PTFE EVA Neoprene Isoprene Polyurethane Leatherher L L MFA, 04 P PE PE

Glassassss Glass Po P Ti al PS PP P T PS PS T Search region

E1/33///ρ

Figure 6.4 Materials for telescope mirrors Glass is better than most metals, among

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Some of the choices — polystyrene foam or CFRP — may at first seem impractical But the potential cost-saving (the factor of 16) is so vast that they are worth examining There are ways of casting a thin film of silicone rubber or of epoxy onto the surface of the mirror-backing (the polystyrene or the CFRP) to give an optically smooth surface that could be silvered The most obvious obstacle is the lack of stability of polymers — they change dimensions with age, humidity, temperature, and so on But glass itself can be reinforced with car-bon fibers; and it can also be foamed to give a material that is denser than polystyrene foam but much lighter than solid glass Both foamed and carbon-reinforced glass have the same chemical and environmental stability as solid glass They could provide a route to large cheap mirrors

Postscript There are, of course, other things you can The stringent design criterion ( <10mm) can be partially overcome by engineering design without reference to the material used The 8.2 m Japanese telescope on Mauna Kea, Hawaii and the very large telescope (VLT) at Cerro Paranal Silla in Chile each have a thin glass reflector supported by an array of hydraulic or piezo-electric jacks that exert distributed forces over its back surface, controlled to vary with the attitude of the mirror The Keck telescope, also on Mauna Kea, is seg-mented, each segment independently positioned to give optical focus But the limitations of this sort of mechanical system still require that the mirror meet a stiffness target While stiffness at minimum weight is the design requirement, the material-selection criteria remain unchanged

Radio telescopes not have to be quite as precisely dimensioned as optical ones because they detect radiation with a longer wavelength But they are much bigger (60 m rather than m) and they suffer from similar distortional Table 6.4 Mirror backing for 200-in (5.1 m) telescope

Material M¼E1/3/ (GPa)1/3.m3/Mg

m (tonne) 2R¼5.1m (from equation (6.4))

Comment

Steel (or Speculum) 0.74 73.6 Very heavy The original choice

GFRP 1.5 25.5 Not dimensionally stable

enough — use for radio telescope

Al-alloys 1.6 23.1 Heavier than glass, and with high thermal expansion

Glass 1.7 21.6 The present choice

Mg-alloys 1.9 17.9 Lighter than glass but high thermal expansion

CFRP 3.0 Very light, but not dimensionally

stable; use for radio telescopes

Foamed polystyrene

4.5 Very light, but dimensionally

unstable Foamed glass?

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problems Microwaves have wavelengths in the mm band, requiring precision over the mirror face of 0.25 mm A recent 45 m radio telescope built for the University of Tokyo achieves this, using CFRP Its parabolic surface is made of 6000 CFRP panels, each servo controlled to compensate for macro-distortion Recent telescopes have been made from CFRP, for exactly the reasons we deduced

Related case studies

6.16 Materials to minimize thermal distortion in precision devices

6.4 Materials for table legs

Luigi Tavolino, furniture designer, conceives of a light-weight table of daring simplicity: a flat sheet of toughened glass supported on slender, un-braced, cylindrical legs (Figure 6.5) The legs must be solid (to make them thin) and as light as possible (to make the table easier to move) They must support the table top and whatever is placed upon it without buckling (Table 6.5) What materials could one recommend?

The model This is a problem with two objectives2: weight is to be minimized, and slenderness maximized There is one constraint: resistance to buckling Consider minimizing weight first

The leg is a slender column of material of density and modulus E Its length, L, and the maximum load, F, it must carry are determined by the design: they are fixed The radius r of a leg is a free variable We wish to minimize the massmof the leg, given by the objective function

mẳr2L 6:6ị

subject to the constraint that it supports a loadPwithout buckling The elastic buckling loadFcritof a column of lengthLand radiusr(see Appendix A) is

Fcrit¼

2EI

L2 ¼

3Er4

4L2 6:7ị

usingIẳr4/4 whereIis the second moment of the area of the column The loadFmust not exceedFcrit Solving for the free variable,r, and substituting it into the equation formgives

m 4F

1=2

ðLÞ2 E1=2

h i

ð6:8Þ

2

(127)

The material properties are grouped together in the last pair of brackets The weight is minimized by selecting the subset of materials with the greatest value of the material index

M1¼

E1=2

(a result we could have taken directly from Appendix B)

Now slenderness Inverting equation (6.7) withFcritset equal toFgives an equation for the thinnest leg that will not buckle:

r 4F

3

1=4

ðLÞ1=2 E

1=4

ð6:9Þ

The thinnest leg is that made of the material with the largest value of the material index

M2¼E

Table 6.5 Design requirements for table legs

Function Column (supporting compressive loads)

Must not buckle under design loads Must not fracture if accidentally struck

Objective Minimize the mass,m

Maximize slenderness

Free variables Diameter of legs, 2r

Choice of material

L

2r

Figure 6.5 A light-weight table with slender cylindrical legs Lightness and slenderness are independent design goals, both constrained by the requirement that the legs must not buckle when the table is loaded The best choice is a material with high values of both

E1/2/andE

(128)

The selection We seek the subset of materials that have high values ofE1/2/ andE We need the Echart again (Figure 6.6) A guideline of slope is drawn on the diagram; it defines the slope of the grid of lines for values of

E1/2/ The guideline is displaced upwards (retaining the slope) until a rea-sonably small subset of materials is isolated above it; it is shown at the position

M1¼5 GPa1/2/(Mg/m3) Materials above this line have higher values of M1 They are identified on the figure:woods(the traditional material for table legs),

composites(particularly CFRP) and certainengineering ceramics Polymers are out: they are not stiff enough; metals too: they are too heavy (even magnesium alloys, which are the lightest) The choice is further narrowed by the require-ment that, for slenderness,Emust be large A horizontal line on the diagram links materials with equal values ofE; those above are stiffer Figure 6.6 shows that placing this line atM1¼100 GPa eliminates woods and GFRP If the legs must be really thin, then the short-list is reduced to CFRP and ceramics: they give legs that weigh the same as the wooden ones but are barely half as thick Ceramics, we know, are brittle: they have low values of fracture toughness

E1/3 ρ E1/2 ρ E ρ

104m/s

103m/s

102 m/s Longitudinal wave speed Guidelines for minimum mass design D

0 0011

Y oo uu nn gg ''sm o s mo dd uu lluu sEs , E ((GG P a )

100-44

0.1 10

10-3 10-2 10-1 10 100 1000 Polyester Polyest P y Foams Polymers and elastomersy Metals Technical ceramics Composites Natural materials Lead alloys W alloysalloys Steels

Ti alloys

Mg alloyso M ll M CFRP C GFRP Al alloys A mer mer Rigid polym foams Flexible polymer foams

Ni alloysalloys

Cu alloysy

Zinc alloysalloys PA PEEK PMMA PC PET Cork Wood Butyl rubber Silicone elastomers e Concretee WC WC Al2O3

B4C

Epoxies PS PTFE EVA Neoprenee Isoprene Polyurethane Leatherher L L MFA, 04 PP PE PE

Glassassss Glass P P P s s Ni s ys s ys Search region

E1/22///ρ

Mg alloys M o Mg alloyso

GFRP Metals E

(129)

Table legs are exposed to abuse — they get knocked and kicked; common sense suggest that an additional constraint is needed, that of adequate toughness This can be done using Figure 4.7; it eliminates ceramics, leaving CFRP The cost of CFRP (Figure 4.17) may cause Snr Tavolino to reconsider his design, but that is another matter: he did not mention cost in his original specification It is a good idea to lay out the results as a table, showing not only the materials that are best, but those that are second-best — they may, when other considerations are involved, become the best choice Table 6.6 shows the way to it

Postscript Tubular legs, the reader will say, must be lighter than solid ones True; but they will also be fatter So it depends on the relative importance Snr Tavolino attaches to his two objectives — lightness and slenderness — and only he can decide that If he can be persuaded to live with fat legs, tubing can be considered — and the material choice may be different Materials selection when section-shape is a variable comes in Chapter 11

Ceramic legs were eliminated because of low toughness If (improbably) the goal was to design a light, slender-legged table for use at high temperatures, ceramics should be reconsidered The brittleness problem can be by-passed by protecting the legs from abuse, or by pre-stressing them in compression Related case

studies

6.2 Materials for oars

6.3 Mirrors for large telescopes 12.2 Spars for man-powered planes 12.4 Forks for a racing bicycle 12.7 Table legs again: thin or light?

6.5 Cost: structural materials for buildings

The most expensive thing that most people buy is the house they live in Roughly half the cost of a house is the cost of the materials of which it is made, and they are used in large quantities (family house: around 200 tonnes; large apartment block: around 20,000 tonnes) The materials are used in three ways: Table 6.6 Materials for table legs

Material TypicalM1

(GPa1/2.m3/Mg)

TypicalM2

GPa

Comment

GFRP 2.5 20 Cheaper than CFRP, but lowerM1andM2

Woods 4.5 10 OutstandingM1; poorM2

Cheap, traditional, reliable

Ceramics 6.3 300 OutstandingM1andM2 Eliminated by brittleness

CFRP 6.6 100 OutstandingM1andM2, but expensive

(130)

structurally to hold the building up; as cladding, to keep the weather out; and as ‘‘internals’’, to insulate against heat, sound, and so forth

Consider the selection of materials for the structure (Figure 6.7) They must be stiff, strong, and cheap Stiff, so that the building does not flex too much under wind loads or internal loading Strong, so that there is no risk of it collapsing And cheap, because such a lot of material is used The structural frame of a building is rarely exposed to the environment, and is not, in general, visible, so criteria of corrosion resistance or appearance are not important here The design goal is simple: strength and stiffness at minimum cost To be more specific: consider the selection of material for floor beams Table 6.7 summarizes the requirements

The model The material index for a stiff beam of minimum mass, m, was developed in Chapter (equations (5.6)–(5.9)) The costCof the beam is just its mass,m, times the cost per kg,Cm, of the material of which it is made:

CẳmCmẳALCm 6:10ị

which becomes the objective function of the problem Proceeding as in Chapter 5, we find the index for a stiff beam of minimum cost to be:

M1¼

E1=2

pCm

The index when strength rather than stiffness is the constraint was not derived earlier Here it is The objective function is still equation (6.10), but the

Floor Joists

(131)

constraint is now that of strength: the beam must support Fwithout failing The failure load of a beam (Appendix A, Section A.4) is:

Ff ẳC2

If ymL

6:11ị

whereC2is a constant,fis the failure strength of the material of the beam and ymis the distance between the neutral axis of the beam and its outer filament for a rectangular beam of depthdand widthb) We assume the proportions of the beam are fixed so thatd¼bwhereis the aspect ratio, typically Using this andI¼bd3/12 to eliminateAin equation (6.10) gives the cost of the beam that will just support the loadFf:

C¼

ffiffiffiffi

p C2

Ff L2

2=3

ðL3Þ Cm

2f=3

" #

ð6:12Þ

The mass is minimized by selecting materials with the largest values of the index

M2¼

2f=3

Cm

The selection Stiffness first Figure 6.8(a) shows the relevant chart: modulusE

against relative cost per unit volume,Cm(the chart uses a relative costCR, defined in Chapter 4, in place of Cm but this makes no difference to the selection) The shaded band has the appropriate slope forM1; it isolates con-crete, stone, brick, woods, cast irons, and carbon steels Figure 6.8(b) shows strength against relative cost The shaded band —M2this time — gives almost the same selection They are listed, with values, in Table 6.8 They are exactly the materials with which buildings have been, and are, made

Postscript Concrete, stone, and brick have strength only in compression; the form of the building must use them in this way (columns, arches) Wood, steel, and reinforced concrete have strength both in tension and compression, and steel, additionally, can be given efficient shapes (I-sections, box sections, tubes, Table 6.7 Design requirements for floor beams

Function Floor beam

Stiffness: must not deflect too much under design loads Strength: must not fail under design loads

Objective Minimize the cost,C

Free variables Cross-section area of beam,A

Choice of material

(132)

Relaattiivvevvvv coecostst ppeerr uunniitt vvovvvv lluoumme, Ce Cv,R Y oo u nn gg ''sm o s mo dd u llu sEs, E (( GG PP a )

0.001 0.1 11 1010 100

0.001 0.1 10 100 1000 (a) E1/3 Cv,Rv R

E1/2 Cv,R E Cv,R Guidelines for minimum cost design Foams olymers Pooo Polymers Metalss Technical ceramics Compositese Natural materials

Leadead alloyseadeadaaaa

W alloys Carbon steelss

Ti alloysi

Mg alloyssss CFRP GFRP Al alloys Al alloys Rigid polymer foams Flexible polymer foamsfoams Zinc alloys PS PTFE PC Wood

Silicone lic elastomers ela s Concrete

Al2O3

SiC Si33N44

Modulus - Relative cost/vol

B44C

PP EVA Polyurethanee Leather Non-technical ceramicsceramics MFA, 04 Cast irons WC Soda glass Sil Silica glassg Sil Sil

Silic

Stonen Brick

ABS Epoxieso Epoxies Ionomers AlN Stainless Stainless steels PEEK PE PE PMMA PM PM PM Polyurethanes Acetal // grain grain T Elastomers ymer er A icon T lym er lic lym er Search region

M1= E1/22/CRρ

Strength,St reng th , σf ((MM PP a ))

0.001 0.1 11 1010 1000

0.001 0.1 10 100 1000 10000

Relativvevvvv coecostst ppeerr uunniitt vvovvvv lluoumme, Ce Cv,RR

Foams Polymers and elastomers Metals Technical ceramics Compositesp C Natural materials Lead alloys W alloys Carbon steels Ti alloys Mg alloys M CFRP GFRP Al alloys Rigid polymer foams me Flexible polymolymolymolym

foamssss

Cu alloys Zinc alloys PS PTFE Cork Wood

Silicone o elastomerso Concrencretencrencre

Al2O3 SiC Si3N4

Strength - Relative cost/vol

e

B4C P

Neolprenen Leather

Non-technical ceramics

MFA, 04,

Cast irons WC Silica glass Silicon tone Brick B AB A A A xies E Ep E E E E E E

Ionomersmersmersmers

AlN Stainless steels PEEKK P // grain grain gra T T σf 1/2 1/2 f Cv,R σf 2/3 f Cv,R σff Cv,R Guidelines for minimum cost design er mer C PS PP Com Sto ABS ABS E Epoxie Ep Ep Stainles steel PE n er yme P PS C AB A E Ep E E Sta P in C Search region M2

M = 2 σ2/3y3/CRρ (b)

(133)

discussed in Chapter 11); the form of the building made from these has much greater freedom

It is sometimes suggested that architects live in the past; that in the late 20th century they should be building with fiberglass (GFRP), aluminum alloys and stainless steel Occasionally they do, but the last two figures give an idea of the penalty involved: the cost of achieving the same stiffness and strength is between and 20 times greater Civil construction (buildings, bridges, roads, and the like) is materials-intensive: the cost of the material dominates the product cost, and the quantity used is enormous Then only the cheapest of materials qualify, and the design must be adapted to use them

Further reading Cowan, H.J and Smith, P.R (1988)The Science and Technology of Building Materials, Van Nostrand-Reinhold, New York

Doran, D.K (1992) The Construction Reference Book, Butterworth-Heinemann, Oxford, UK

6.2 Materials for oars 6.4 Materials for table legs

12.5 Floor joists: wood, bamboo or steel?

6.6 Materials for flywheels

Flywheels store energy Small ones — the sort found in children’s toys — are made of lead Old steam engines have flywheels; they are made of cast iron Cars have them too (though you cannot see them) to smooth power-trans-mission More recently flywheels have been proposed for power storage and regenerative braking systems for vehicles; a few have been built, some of high-strength steel, some of composites Lead, cast iron, steel, composites — there is a strange diversity here Whatisthe best choice of material for a flywheel?

Table 6.8 Structural materials for buildings

Material M1

(GPa1/2/(kg/m3))

M2

(MPa2/3(kg/m3))

Comment

Concrete 160 14

Brick 12 12 Use in compression only

Stone 9.3 12

Woods 21 90 Tension and compression, with

freedom of section shape

Cast Iron 17 90

Steel 14 45

(134)

An efficient flywheel stores as muchenergy per unit weight as possible As the flywheel is spun up, increasing its angular velocity,!, it stores more energy The limit is set by failure caused by centrifugal loading: if the centrifugal stress exceeds the tensile strength (or fatigue strength), the flywheel flies apart One constraint, clearly, is that this should not occur

The flywheel of a child’s toy is not efficient in this sense Its velocity is limited by the pulling-power of the child, and never remotely approaches the burst velocity In this case, and for the flywheel of an automobile engine — we wish to maximize theenergy stored per unit volumeat a constant (specified)angular velocity There is also a constraint on the outer radius,R, of the flywheel so that it will fit into a confined space

The answer therefore depends on the application The strategy for optimizing flywheels for efficient energy-storing systems differs from that for children’s toys The two alternative sets of design requirements are listed in Table 6.9(a) and (b)

The model An efficient flywheel of the first type stores as much energy per unit weight as possible, without failing Think of it as a solid disk of radiusRand thicknesst, rotating with angular velocity!(Figure 6.9) The energyUstored in the flywheel is (Appendix A)

U¼1

2J!

2 6:13ị

HereJẳ(/2)R4tis the polar moment of inertia of the disk andthe density of the material of which it is made, giving

Uẳ

4R

4t!2 6:14ị

Table 6.9 Design requirements for maximum-energy flywheel and fixed velocity

(a) For maximum-energy flywheel

Function Flywheel for energy storage

Constraints Outer radius,R, fixed

Must not burst

Adequate toughness to give crack-tolerance

Objective Maximize kinetic energy per unit mass

(b) For fixed velocity

Function Flywheel for child’s toy

Constraints Outer radius,R, fixed

Objective Maximize kinetic energy per unit volume at fixed angular velocity

(135)

The mass of the disk is

m¼R4t ð6:15Þ

The quantity to be maximized is the kinetic energy per unit mass, which is the ratio of the last two equations:

U m¼

1 4R

2!2 ð6:16Þ

As the flywheel is spun up, the energy stored in it increases, but so does the centrifugal stress The maximum principal stress in a spinning disk of uniform thickness (Appendix A) is

maxẳ

3ỵv

8

R2!21

2R

2!2 ð6:17Þ

where is Poisson’s ratio (1/3) This stress must not exceed the failure stressf(with an appropriate factor of safety, here omitted) This sets an upper limit to the angular velocity, !, and disk radius, R (the free variables) EliminatingR!between the last two equations gives

U m¼

1

f

ð6:18Þ

The best materials for high-performance flywheels are those with high values of the material index

Mẳf

6:19ị

It has units of kJ/kg

And now the other sort of flywheel — that of the child’s toy Here we seek the material that stores the most energy per unit volume V at constant

Material Density ρ

Strength σ

Burst shield Flywheel

t R ω Stress

σ=ρR 2

ω2

2

Figure 6.9 A flywheel The maximum kinetic energy it can store is limited by its strength

(136)

velocity,! The energy per unit volume at a given!is (from equation (6.2)):

U V¼

1 4R

2!2

BothRand!are fixed by the design, so the best material is now that with the greatest value of

M2ẳ 6:20ị

The selection Figure 6.10 shows the strength — density chart Values ofM1

correspond to a grid of lines of slope One such is plotted as a diagonal line at the valueM1¼200 kJ/kg Candidate materials with high values ofM1lie in

the search region towards the top left The best choices are unexpected ones: composites, particularly CFRP, high strength titanium alloys and some ceramics, but these are ruled out by their low toughness

But what of the lead flywheels of children’s toys? There could hardly be two more different materials than CFRP and lead: the one, strong and light,

D

Densiitty,ρ ((MMg//m3)

0.0011

Strength, trength , σσf ((MM PP aa ))

0.0011

10

0.1 11

0.1 10 100 1000 10000 Foams Polymers and elastomers Metals Ceramics Composites Natural N materials Lead alloys Tungsten alloysalloys lss S Ti alloy

Mg alloyso CFRPF GFRPF Al alloys polymm Rigid poly Rigid pol foa Flexible polymer foams Ni allo Copperpp alloys Zinc allo PA PEEKE PMMA PC TT

Cork Wood Butyl rubberr Silicone elastomers Concrete Tungsten carbide Al2O3

SiC Si3N4 Strength - Density

MFA, 04

fo e po oys σf 1/2 f ρ σf 2/3 f ρ σff ρ Guidelines for minimum mass design

Metals and polymers: yield strength Ceramics and glasses: MOR Elastomers: tensile tear strength Composites: tensile failure

Foam ials polymermer foams A PMMA PC ood K PETT Metals Ni alloys rials

d polyml fo PA PC Wood EK Met Ni allo Search region

M1= σ

f///ρ

M2=ρ

oys Stee ys E e e Search region

(137)

the other, soft and heavy Why lead? It is because, in the child’s toy, the constraint is different Even a super-child cannot spin the flywheel of his toy up to its burst velocity The angular velocity ! is limited instead by the drive mechanism (pull-string, friction drive) Then as we have seen, the best material is that with the largest density The second selection line on Figure 6.10 shows the indexM2at the value 10 Mg/m3 We seek materials in Search Area to the

right of this line Lead is good Cast iron is less good, but cheaper Gold, platinum, and uranium (not shown on the chart) are better, but may be thought unsuitable for other reasons

Postscript A CFRP rotor is able to store around 400 kJ/kg A lead flywheel, by

contrast, can store only kJ/kg before disintegration; a cast-iron

flywheel, about 30 All these are small compared with the energy density in gasoline: roughly 20,000 kJ/kg Even so, the energy density in the flywheel is considerable; its sudden release in a failure could be catastrophic The disk must be surrounded by a burst-shield and precise quality control in manu-facture is essential to avoid out-of-balance forces This has been achieved in a number of composite energy-storage flywheels intended for use in trucks and buses, and as an energy reservoir for smoothing wind-power generation

And now a digression: the electric car Hybrid petrol-electric cars are already on the roads, using advanced lead-acid battery technology to store energy But batteries have their problems: the energy density they can contain is low (see Table 6.10); their weight limits both the range and the performance of the car It is practical to build flywheels with an energy density of roughly equal to that of the best batteries Serious consideration is now being given to a flywheel for electric cars A pair of counter-rotating CFRP disks are housed in a steel burst-shield Magnets embedded in the disks pass near coils in the housing, inducing a current and allowing power to be drawn to the electric motor that drives the

Table 6.10 Energy density of power sources

Source Energy density

(kJ/kg)

Comment

Gasoline 20,000 Oxidation of hydrocarbon — mass of

oxygen not included

Rocket fuel 5000 Less than hydrocarbons because oxidizing

agent forms part of fuel

Flywheels Up to 400 Attractive, but not yet proven

Lithium-ion battery Up to 350 Attractive but expensive, and with limited

life

Nickel-cadmium battery 170–200

Lead-acid battery 50–80 Large weight for acceptable range

Springs rubber bands Up to Much less efficient method of energy

storage than flywheel

6.6 Materials for flywheels 125

(138)

wheels Such a flywheel could, it is estimated, give an electric car an adequate range, at a cost competitive with the gasoline engine and with none of the local pollution

Further reading Christensen, R.M (1979)Mechanics of Composite Materials, Wiley Interscience, New York, p 213 et seq

Lewis, G (1990)Selection of Engineering Materials, Part 1, Prentice Hall, NJ, p Medlicott, P.A.C and Potter, K.D (1986) The development of a composite flywheel for

vehicle applications, in Brunsch, K., Golden, H-D., and Horkert, C-M (eds) High Tech—the Way into the Nineties, Elsevier, Amsterdam, p 29

6.7 Materials for springs 6.11 Safe pressure vessels

10.2 Multiple constraints: con-rods for high performance engines

6.7 Materials for springs

Springs come in many shapes (Figure 6.11 and Table 6.11) and have many purposes: think of axial springs (e.g a rubber band), leaf springs, helical springs, spiral springs, torsion bars Regardless of their shape or use, the best material for a spring of minimum volume is that with the greatest

F

(a)

(b)

(c)

(d)

Figure 6.11 Springs store energy The best material for any spring, regardless of its shape or the way

in which it is loaded, is that with the highest value off

2

/E, or, if weight is important,

(139)

value of 2f=E, and for minimum weight it is that with the greatest value of

2f=E(derived below) We use them as a way of introducing two of the most

useful of the charts: Young’s modulusEplotted against strengthf, and specific

modulusE/plotted against specific strengthf/(Figures 4.5 and 4.6)

The model The primary function of a spring is to store elastic energy and —

when required — release it again The elastic energy stored per unit volume in

a block of material stressed uniformly to a stressis

Wv¼

1

2

E ð6:21Þ

where E is Young’s modulus We wish to maximize Wv The spring will be

damaged if the stressexceeds the yield stress or failure stressf; the constraint

is < f Thus the maximum energy density is Wv¼

1

2f

E ð6:22Þ

Torsion bars and leaf springs are less efficient than axial springs because much of the material is not fully loaded: the material at the neutral axis, for instance, is not loaded at all For leaf springs

Wv¼

1

2f

E and for torsion bars

Wv¼

1

2f

E

But — as these results show — this has no influence on the choice of material The best stuff for a spring regardless of its shape is that with the biggest value of

M1¼

2f

E ð6:23Þ

If weight, rather than volume, matters, we must divide this by the density

(giving energy stored per unit weight), and seek materials with high values of M2¼

2f

E ð6:24Þ

Table 6.11 Design requirements for springs

Function Elastic spring

Constraints No failure, meaning < fthroughout the spring

Objective Maximum stored elastic energy per unit volume, or

Maximum stored elastic energy per unit weight

(140)

The selection The choice of materials for springs of minimum volume is shown in Figure 6.12(a) A family lines of slope link materials with equal

values of M1¼2f=E; those with the highest values of M1 lie towards the

bottom right The heavy line is one of the family; it is positioned so that a

subset of materials is left exposed The best choices are ahigh-strength steel

lying near the top end of the line Other materials are suggested too: CFRP

(now used for truck springs),titanium alloys(good but expensive), andnylon

(children’s toys often have nylon springs), and, of course, elastomers Note

how the procedure has identified a candidate from almost every class of materials: metals, polymers, elastomers and composites They are listed, with commentary, in Table 6.12(a)

Materials selection for light springs is shown in Figure 6.12(b) A family of lines of slope link materials with equal values of

M2¼

f

E

ẳ

2f

E 6:25ị

Strength, Strength σσf f((MMPPaa)

YY o u n g 's mo d u lu s, E ( G PP a )

0 11 1010 100 1000

0.01 0.1 10 100 1000

= 10-4

Yield strain Y σf E 10-3 10-2 1000-1-1-1-1

Non-technical ceramics MFA, 04 Foams Polymers Metals Technical ceramics Composites

Lead alloysead y

W alloys

Ti alloys

Mg alloysy CFRP

GFRP Al alloyso

Rigid polymer foams Ni alloys Cu alloys Cu a Zinc alloys Z PMMAA Cork Wo W Wo Polyurethane SiliconeS elastomers Concreter

Al22O3

SiC

AlN Modulus - Strength

B4C

EVA eather

Cast irons WCC

Silicon S

Stone Brickk

Epoxies

Ionomers

Steelss

Polyurethaneoolyu

PA PCC PE PTFE PS P PP P Phenolic Metals and polymers: yield strength

ne σf E

σff E σf3/222

E Design guidelines Buckling before yield Yield before buckling Elastomers W a W ood oo Siliconl elastoa Lea I

Phenh n

al on sto ea Io al on sto ea Io en Search region σf /E

2

(141)

One is shown at the valueM2¼2 kJ/kg Metals, because of their high density,

are less good than composites, and much less good than elastomers (You can store roughly eight times more elastic energy, per unit weight, in a rubber band than in the best spring steel.) Candidates are listed in Table 6.12(b) Wood —

the traditional material for archery bows, now appears

Postscript Many additional considerations enter the choice of a material for a

spring Springs for vehicle suspensions must resist fatigue and corrosion; engine Specific strength, σf/ρ (MPa/(kg/m3))

S p e c if ic m oo dd uu lluu sE / s , E/ ρρ (GPa/(kg/m(GPa 3)) 10

10 10-3 10-2 1 10

10-555 10-444 1-333

0 1-222 10-1

= 10-4

Yield strain σf E 10-3 10-2 N Non-technical ceramics Foams Polymers Metals Technical ceramics Composites Lead alloys Ti alloys Mg alloys CFRP C GFRP

Al alloyss A A A Rigid polymer Rigid polymer foams Cu alloys C

Zinc alloysc

PMMAA Wood

Polyurethanee

Silicones e Concrete

Al2O3

SiCC AlN Specific modulus - Specific strength

B4C

EVA Leather

Cast irons Cast irons WCC

Soda glassd Silica glassl

Silicon Stone Brick Epoxiesox Epoxiespoxi Ionomers Steels PA PC P PE PTFE PS P PP

Si3NN44

Cork

MFA, 04 Metals and polymers: yield strength

Po a σf2 E

σff E

σf3/222 E Design guidelines Buckling before yield Yield before buckling Elastomers Search region σf σ σ2/// E//ρ

Figure 6.12(b) Materials for light springs Metals are disadvantaged by their high densities Composites are good; so is wood Elastomers are excellent

Table 6.12(a) Materials for efficient small springs

Material M1¼2f=E

(MJ/m3)

Comment

Ti alloys –12 Expensive, corrosion-resistant

CFRP 6–10 Comparable in performance with steel; expensive

Spring steel 3–7 The traditional choice: easily formed and heat treated

Nylon 1.5–2.5 Cheap and easily shaped, but high loss factor

Rubber 20–50 Better than spring steel; but high loss factor

(142)

valve-springs must cope with elevated temperatures A subtler property is the loss coefficient, shown in Figure 4.9 Polymers have a relatively high loss factor and dissipate energy when they vibrate; metals, if strongly hardened, not Polymers, because they creep, are unsuitable for springs that carry a steady load, though they are still perfectly good for catches and locating springs that spend most of their time unstressed

Further reading Boiton, R.G (1963) The mechanics of instrumentation,Proc Int Mech Eng.177(10), 269–288

Hayes, M (1990) Materials update 2: springs,Engineering, May, p 42 Related case

studies

6.8 Elastic hinges and couplings 12.3 Ultra-efficient springs

12.8 Shapes that flex: leaf and strand structures 14.4 Connectors that not relax their grip

6.8 Elastic hinges and couplings

Nature makes much use of elastic hinges: skin, muscle, cartilage all allow large,

recoverable deflections Man, too, design with flexure and torsion hinges:

ligaments that connect or transmit load between components while allowing limited relative movement between them by deflecting elastically (Figure 6.13 and Table 6.13) Which materials make good hinges?

The model Consider the hinge for the lid of a box The box, lid and hinge

are to be molded in one operation The hinge is a thin ligament of material that flexes elastically as the box is closed, as in the figure, but it carries no significant axial loads Then the best material is the one that (for given ligament Table 6.12(b) Materials for efficient light springs

Material M1¼2f=E

(kJ/kg)

Comment

Ti alloys 0.9–2.6 Better than steel; corrosion-resistant; expensive

CFRP 3.9–6.5 Better than steel; expensive

GFRP 1.0–1.8 Better than spring steel; less expensive than CFRP

Spring steel 0.4 –0.9 Poor, because of high density

Wood 0.3–0.7 On a weight basis, wood makes good springs

Nylon 1.3–2.1 As good as steel, but with a high loss factor

Rubber 18–45 Outstanding; 20 times better than spring steel; but with

(143)

dimensions) bends to the smallest radius without yielding or failing When a

ligament of thicknesstis bent elastically to a radiusR, the surface strain is

"ẳ t

2R 6:26ị

and since the hinge is elastic — the maximum stress is

¼E t

2R ð6:27Þ

This must not exceed the yield or failure strengthf Thus the minimum radius

to which the ligament can be bent without damage is

R1

2 E

f

ð6:28Þ

The best material is the one that can be bent to the smallest radius, that is, the one with the greatest value of the index

Mẳf

E 6:29ị

L b

t

Figure 6.13 Elastic or ‘‘natural’’ hinges The ligaments must bend repeatedly without failing The cap of a shampoo bottle is an example; elastic hinges are used in high performance applications too, and are found widely in nature

Table 6.13 Design requirements for elastic hinges

Function Elastic hinge

Constraints No failure, meaning < fthroughout the hinge

Objective Maximize elastic flexure

(144)

The selection We need the fE chart again (Figure 6.14) Candidates are identified by using the guideline of slope 1; a line is shown at the position

M¼f/E¼3102 The best choices for the hinge are all polymeric materials.

The short-list (Table 6.14) includes polyethylene, polypropylene, nylon, and, best of all, elastomers, though these may be too flexible for the body of the box

Strength, Strength σσff((MMPPaa)

YY o u n g 's mo d u lu s , E (G PP a )

0 11 1010 100 1000 0.01 0.1 10 100 1000

= 10-4

Yield strain Y σf E 10-3 10-2 1000-1-1-1-1

Non-technical ceramics MFA, 04 Foams Polymers Metals Technical ceramics Composites

Lead alloysy Lead

W alloys W

Ti alloys

Mg alloysy FRP

FRP

Al alloyso

Rigid polymer foams Ni alloys Cu alloys Cu a Zinc alloys Z PMMAA Cork Wood W Woo Polyurethane Silicone Sl

Al22O3

SiC

AlN Modulus - Strength

B4C

EVA Leather

Cast irons WCC

Soda glassoda Silica glasslica

Silicon S

Stone Brickk

Epoxies Ionomers Steelss Polyurethaneo Polyu PA PCC PE PTFE PS PS PP Phenolic Metals and polymers: yield strength

e σf E

σff E σf3/2222

E Design guidelines Buckling before yield Yield before buckling Elastomers GFR Phenolih Ti alloys CFR A loys Zi Z C FRP olic ys M FRP Al Zin Z Ca FR noli oys FR A Zi Z Ca Search region

σf /E

Figure 6.14 Materials for elastic hinges Elastomers are best, but may not be rigid enough to meet other design needs Then polymers such as nylon, PTFE and PE are better Spring steel is less good, but much stronger

Table 6.14 Materials for elastic hinges

Material M

(103)

Comment

Polyethylene 32 Widely used for cheap hinged bottle caps, etc

Polypropylene 30 Stiffer than polyethylene Easily molded

Nylon 30 Stiffer than polyethylene Easily molded

PTFE 35 Very durable; more expensive than PE, PP, etc

Elastomers 100–1000 Outstanding, but low modulus

High strength copper alloys

4 Mless good than polymers Use when high tensile stiffness is required

(145)

itself Cheap products with this sort of elastic hinge are generally molded from polyethylene, polypropylene, or nylon Spring steel and other metallic spring materials (like phosphor bronze) are possibilities: they combine usable f/E with high E, giving flexibility with good positional stability (as in the suspensions of relays) Table 6.14 gives further details

Postscript Polymers give more design-freedom than metals The elastic hinge

is one example of this, reducing the box, hinge and lid (3 components plus the fasteners needed to join them) to a single box-hinge-lid, molded in one operation Their spring-like properties allow snap-together, easily-joined parts Another is the elastomeric coupling — a flexible universal joint, allowing high angular, parallel, and axial flexibility with good shock absorption character-istics Elastomeric hinges offer many opportunities, to be exploited in engi-neering design

6.7 Materials for springs 6.9 Materials for seals

6.10 Deflection-limited design with brittle polymers 12.8 Shapes that flex: leaf and strand structures

6.9 Materials for seals

A reusable elastic seal consists of a cylinder of material compressed between two flat surfaces (Figure 6.15) The seal must form the largest possible contact width,b, while keeping the contact stress, , sufficiently low that it does not damage the flat surfaces; and the seal itself must remain elastic so that it can be

Force f / Unit Length

Contact Stress

σ

Seal

b

b Rigid

clamp Seal: modulus E⬘ strength σy

2R

Figure 6.15 An elastic seal A good seal gives a large conforming contact-area without imposing damaging loads on itself or on the surfaces with which it mates

(146)

reused many times What materials make good seals? Elastomers — everyone know that But let us the job properly; there may be more to be learnt We build the selection around the requirements of Table 6.15

The model A cylinder of diameter 2Rand modulusE, pressed on to a rigid flat

surface by a force f per unit length, forms an elastic contact of width b (Appendix A) where

b2 fR

E 1=3

ð6:30Þ

This is the quantity to be maximized: the objective function The contact stress, both in the seal and in the surface, is adequately approximated (Appendix A) by

ẳ0:6 fE R

1=3

6:31ị

The constraint: the seal must remain elastic, that is, must be less than the yield or failure strength,f, of the material of which it is made Combining the last two equations with this condition gives

b 3:3R f

E ð6:32Þ

The contact width is maximized by maximizing the index

M1¼

f

E

It is also required that the contact stressbe kept low to avoid damage to the flat surfaces Its value when the maximum contact force is applied (to give the biggest width) is simply f, the failure strength of the seal Suppose the flat surfaces are damaged by a stress of greater than 100 MPa The contact pressure is kept below this by requiring that

M2¼f 100MPa

The selection The two indices are plotted on the fE chart in

Figure 6.16 isolating elastomers, foams and cork The candidates are listed

Table 6.15 Design requirements for elastic seals

Function Elastic seal

Constraints Limit on contact pressure

Low cost

Objective Maximum conformability to surface

(147)

in Table 6.16 with commentary The value of M2¼100 MPa admits all elastomers as candidates If M2 were reduced to 10 MPa, all but the most compliant elastomers are eliminated, and foamed polymers become the best bet

Strength, Strength σσff((MMPPaa)

YY o u n g 's mo d u lu s , E (G PP a )

0 11 1010 100 1000

0.01 0.1 10 100 1000

= 10-4

Yield strain Y

σf

E

10-3

10-2 10000-1-1-1-1

Non-technical ceramics MFA, 04 Foams Polymers Metals Technical ceramics Composites Lead alloysead y

W alloys W

Ti alloys

Mg alloysy CFRP

GFRP Al alloyso

Rigid polymer foams Ni alloys Cu allo Cu a Zinc alloys Z PMMAA Cork Wood W Woo Polyurethane Silicone Sl

Al22O3

SiC AlN Modulus - Strength

B4C

EVA Leather

Cast irons WCC

Silicon S

Stone Brickk

Epoxies

Ionomers

Steelss

Polyurethaneoolyu

PA PCC E PTF PS P PP P nolic Metals and polymers: yield strength

ne σf

E

σff

E σf3/222 E Design guidelines Buckling before yield Yield before buckling Elastomers yure PE FE σ E A GF od Phenoh Ti alloy CF alloys GFR P eno lloys CF Z C GF eno alloy CF Search region

M1= σf///E

y F

M2= σf

Figure 6.16 Materials for elastic seals Elastomers, compliant polymers and foams make good seals

Table 6.16 Materials for reusable seals

Material M1¼Ef Comment

Elastomeric EVA 0.7–1 The natural choice; poor resistance to heat and to some solvents

Polyurethanes 2–5 Widely used for seals

Silicone rubbers 0.2–0.5 Higher temperature capability than carbon-chain elastomers, chemically inert

PTFE 0.05–0.1 Expensive but chemically stable and with high

temperature capability

Polyethylenes 0.02–0.05 Cheap but liable to take a permanent set

Polypropylenes 0.2–0.04 Cheap but liable to take a permanent set

Nylons 0.02–0.03 Near upper limit on contact pressure

Cork 0.03–0.06 Low contact stress, chemically stable

Polymer foams up to 0.03 Very low contact pressure; delicate seals

(148)

Postscript The analysis highlights the functions that seals must perform: large contact area, limited contact pressure, environmental stability Elastomers maximize the contact area; foams and cork minimize the contact pressure; PTFE and silicone rubbers best resist heat and organic solvents The final choice depends on the conditions under which the seal will be used

6.7 Materials for springs 6.8 Elastic hinges and couplings

6.10 Deflection-limited design with brittle polymers

Among mechanical engineers there is a rule-of-thumb: avoid materials with plane–strain fracture toughnessesK1Cless than 15 MPa.m1/2 Almost all metals pass: they have values of K1C in the range of 20–100 in these units White cast iron and some powder-metallurgy products fail; they have values as low as 10 MPa.m1/2 Ordinary engineering ceramics have values in the range 1–6 MPa.m1/2; mechanical engineers view them with deep suspicion But engineering polymers are even less tough, withK1Cin the range 0.5–3 MPa.m1/2 and yet engineers use them all the time What is going on here?

When a brittle material is deformed, it deflects elastically until it fractures The stress at which this happens is

f ¼

CKc

ffiffiffiffiffiffiffi ac

p ð6:33Þ

whereKc is an appropriate fracture toughness,acis the length of the largest crack contained in the material andCis a constant that depends on geometry, but is usually about In aload-limiteddesign a tension member of a bridge, say — the part will fail in a brittle way if the stress exceeds that given by equation (6.33) Here, obviously, we want materials with high values ofKc

But not all designs are load-limited; some are energy-limited, others are deflection limited Then the criterion for selection changes Consider, then, the three scenarios created by the three alternative constraints of Table 6.17

Table 6.17 Design requirements for deflection limited structures Function Resist brittle fracture

Constraints Design load specified or

Design energy specified or

Design deflection specified

Objective Minimize volume (mass, cost)

(149)

The model In load-limited design the component must carry a specified load or pressure without fracturing It is usual to identifyKc, with the plane-strain fracture toughness, K1C, corresponding to the most highly constrained cracking conditions, because this is conservative Then, as equation (6.33) shows, the best choice of materials for minimum volume design are those with high values of

M1ẳK1C 6:34ị

For load-limited design using thin sheet, a plane-stress fracture toughness may be more appropriate; and for multi-layer materials, it may be an interface fracture toughness that matters The point, though, is clear enough: the best materials for load-limited design are those with large values of the appropriateKc

But, as we have said, not all design is load-limited Springs, and contain-ment systems for turbines and flywheels are energy-limited Take the spring (Figure 6.11) as an example The elastic energy per unit volume stored in it is the integral over the volume of

Ue¼

1 2"¼

1

2

E

The stress is limited by the fracture stress of equation (6.33) so that — if ‘‘failure’’ means ‘‘fracture’’ — the maximum energy the spring can store is

Umax

e ¼

C2

2ac

K2

1C

E

For a given initial flaw size, energy is maximized by choosing materials with large values of

M2¼

K2

1C

E Jc ð6:35Þ

whereJcis the toughness (usual units: kJ/m2)

Figure 6.17 Load and deflection-limited design Polymers, having low moduli, frequently require deflection-limited design methods

(150)

There is a third scenario: that ofdisplacement-limiteddesign (Figure 6.17) Snap-on bottle tops, snap together fasteners, and such like are displacement-limited: they must allow sufficient elastic displacement to permit the snap-action without failure, requiring a large failure strainEf The strain is related to the stress by Hooke’s lawE¼/E and the stress is limited by the fracture equation (6.33) Thus the failure strain is

"f ¼

C

ffiffiffiffiffiffiffi ac

p K1C

E ð6:36Þ

The best materials for displacement-limited design are those with large values of

M3¼K1C

E ð6:37Þ

The selection Figure 6.18 shows a chart of fracture toughness,K1C, plotted

against modulusE It allows materials to be compared by values of fracture

100

10

1

0.1

0.01

F rac tur e t oughnes s, K1 C (MP a m 1/ 2)

0.001 0.01 0.1 10 100 1000

0.01 0.1 10 100 1000 Foams Polymers and elastomers Metals Technical ceramics Composites Natural materials Lead alloys W alloys Steels Ti alloys Mg alloys CFRP GFRP Al alloys Rigid polyme R ly foams Flexible polymer foams Ni alloys Cu alloys Zinc alloys PS PTFE PC Cork Wood Butyl rubber Silicone elastomers Concrete

Al2O3

SiC Si3N4

Fracture toughness - Modulus

B4C PP EVA Polyurethane Leather Non-technical ceramics ast irons WC Soda glass Silica glass Silicon Stone Brick ABS Epoxies Ionomers MFA, 04 Design guidelines

Toughness Gc =

(K1C)2/E kJ/m2

Lower limit

for K1C

K1C / E

(K1C)2/ E

Cor

GF

Cast i

M3=K1C/E

merer

Ni alloys

M2= K12C/E Search

region

Figure 6.18 The selection of materials for load, deflection, and energy-limited design

(151)

toughness,M1, by toughness, M2, and by values of the deflection-limited index

M3 As the engineer’s rule-of-thumb demands, almost all metals have values of

K1Cthat lie above the 15 MPa.m1/2 acceptance level for load-limited design,

shown and a horizontal selection line in Figure 6.18 Polymers and ceramics not

The line showing M2 on Figure 6.18 is placed at the value kJ/m2 Materials with values of M2 greater than this have a degree of shock-resis-tance with which engineers feel comfortable (another rule-of-thumb) Metals, composites, and some polymers qualify; ceramics not When we come to deflection-limited design, the picture changes again The line shows the index M3¼K1C/E at the value 103m1/2 It illustrates why polymers ﬁnd such wide application: when the design is deﬂection-limited, polymers — particularly nylons, polycarbonates and polystyrene — are better than the best metals (Table 6.18)

Postscript The figure gives further insights The mechanical engineers’ love of

metals (and, more recently, of composites) is inspired not merely by the appeal of theirK1Cvalues They are good by all three criteria (K1C,K21C=EandK1C/ E) Polymers have good values of K1C/E and are acceptable by K12C=E

Ceramics are poor by all three criteria Herein lie the deeper roots of the engineers’ distrust of ceramics

Further reading Background in fracture mechanics and safety criteria can be found in:

Brock, D (1984) Elementary Engineering Fracture Mechanics, Martinus Nijoff, Boston

Hellan, K (1985)Introduction to Fracture Mechanics, McGraw-Hill

Hertzberg, R.W (1989)Deformation and Fracture Mechanics of Engineering Materials, Wiley, New York

6.7 Materials for springs 6.8 Elastic hinges and couplings 6.11 Safe pressure vessels Table 6.18 Materials fracture-limited design

Design type and rule-of-thumb Material

Load-limited design K1C>15 MPa.m1/2

Metals, polymer-matrix composites Energy-limited design

JC>1 kJ/m2

Metals, composites and some polymers Displacement-limited design

K1C/E>103m1/2

Polymers, elastomers and the toughest metals

(152)

6.11 Safe pressure vessels

Pressure vessels, from the simplest aerosol-can to the biggest boiler, are designed, for safety, to yield or leak before they break The details of this design method vary Small pressure vessels are usually designed to allow general yield at a pressure still too low to cause any crack the vessel may contain to pro-pagate (‘‘yield before break’’); the distortion caused by yielding is easy to detect and the pressure can be released safely With large pressure vessels this may not be possible Instead, safe design is achieved by ensuring that the smallest crack that will propagate unstably has a length greater than the thickness of the vessel wall (‘‘leak before break’’); the leak is easily detected, and it releases pressure gradually and thus safely (Table 6.19) The two criteria lead to different material indices What are they?

The model The stress in the wall of a thin-walled spherical pressure vessel of radiusR(Figure 6.19) is

ẳpR

2t 6:38ị

In pressure vessel design, the wall thickness,t, is chosen so that, at the working pressure p, this stress is less than the yield strength f of the wall A small

R t

p

2 ac

t p R

2 t

σ =

Figure 6.19 A pressure vessel containing a flaw Safe design of small pressure vessels requires that they yield before they break; that of large pressure vessels may require, instead, that they leak before they break

Table 6.19 Design requirements for safe pressure vessels

Function Pressure vessel (contain pressure p safely) Constraints Radius R specified

Objective Maximize safety using yield-before-break criterion, or

(153)

pressure vessel can be examined ultrasonically, or by X-ray methods, or proof tested, to establish that it contains no crack or flaw of diameter greater than 2a

c; then the stress required to make the crack propagate 3is

¼CKffiffiffiffiffiffiffiffi1C

a

c

p

whereCis a constant near unity andK1Cis the plane-strain fracture toughness

Safety can be achieved by ensuring that the working stress is less than this, giving

p 2t R

K1C

ffiffiffiffiffiffiffiffi a

c

p The largest pressure (for a givenR, tanda

c) is carried by the material with the

greatest value of

MlẳK1C 6:39ị

But this design is not fail-safe If the inspection is faulty, or if, for some other reason a crack of length greater thana

cappears, catastrophe follows Greater

security is obtained by requiring that the crack will not propagate even if the stress reaches the general yield stress — for then the vessel will deform stably in a way that can be detected This condition is expressed by settingequal to the yield stressfgiving

ac C2 K1C

f

The tolerable crack size, and thus the integrity of the vessel, is maximized by choosing a material with the largest value of

M2ẳ K1C

f

6:40ị Large pressure vessels cannot always be X-rayed or sonically tested; and proof testing them may be impractical Further, cracks can grow slowly because of corrosion or cyclic loading, so that a single examination at the beginning of service life is not sufficient Then safety can be ensured by arranging that a crack just large enough to penetrate both the inner and the outer surface of the vessel is still stable, because the leak caused by the crack can be detected This is achieved if the stress is always less than or equal to

¼ CKffiffiffiffiffiffiffiffiffiffi1C

t=2

p ð6:41Þ

3

If the wall is sufficiently thin, and close to general yield, it will fail in a plane-stress mode Then the relevant fracture toughness is that for plane stress, not the smaller value for plane strain

(154)

The wall thicknesstof the pressure vessel was, of course, designed to contain the pressurepwithout yielding From equation (6.38), this means that

tpR 2f

ð6:42Þ Substituting this into the previous equation (with¼f) gives

p 4C

R K2

1C

f

ð6:43Þ The maximum pressure is carried most safely by the material with the greatest value of

M3¼ K2

1C

f

ð6:44Þ BothM1andM2could be made large by making the yield strength of the wall,

f, very small: lead, for instance, has high values of both, but you would not choose it for a pressure vessel That is because the vessel wall must also be as thin as possible, both for economy of material, and to keep it light The thinnest wall, from equation (6.42), is that with the largest yield strength,f Thus we wish also to maximize

M4¼f

narrowing further the choice of material

The selection These selection criteria are explored by using the chart shown in Figure 6.20: the fracture toughness, K1C, plotted against elastic limit f The indicesM1,M2,M3andM4appear as lines of slope 0, 1, 1/2 and as lines that are vertical Take ‘‘yield before break’’ as an example A diagonal line corresponding to a constant value ofM1¼K1C/flinks materials with equal performance; those above the line are better The line shown in the figure at M1¼0.6 m1/2 (corresponding to a process zone of size 100 mm) excludes everything but the toughest steels, copper, aluminum and titanium alloys, though some polymers nearly make it (pressurized lemonade and beer containers are made of these polymers) A second selection line atM3¼50 MPa eliminates aluminum alloys Details are given in Table 6.20

The leak-before-break criterion M2¼

K2 1C

f

(155)

Postscript Large pressure vessels are always made of steel Those for models — a model steam engine, for instance — are made of copper It is chosen, even though it is more expensive, because of its greater resistance to corrosion Corrosion rates not scale with size The loss of 0.1 mm through corrosion is not serious in a pressure vessel that is 10 mm thick; but if it is only mm thick it becomes a concern Table 6.20 Materials for safe pressure vessels

Material M1¼KlC/f (m1/2)

M3¼f (MPa)

Comment

Stainless steels 0.35 300 Nuclear pressure vessels are made of grade 316 stainless steel

Low alloy steels 0.2 800 These are standard in this application Copper 0.5 200 Hard drawn copper is used for small

boilers and pressure vessels

Aluminum alloys 0.15 200 Pressure tanks of rockets are aluminum Titanium alloys 0.13 800 Good for light pressure vessels, but

expensive Elaaststiic lic limmiit,tσσff((MMPPaa)

F rra ct u re to u g h n e ss, K Ic ((M P a m 11 /2//)

0.11 1010 100 1000

0.0011 0.1 10 100 1000 100 10 0.1 0.01 1000 Guidelines for safe design

Yield before fracture Fracture before yield Process zone size, mm Non-technic ceramics oams Polymers and elastomers Metals Technical ceramics s Compositess Lead alloys

W alloysys Stainless steelsa s s

Ti alloys Ti a Mg alloys CFRP CFR GFRP Al alloys Rigid polymer foams Flexible polymerble p

foamsfoa

alloys Cu alloysy

Zinc alloysy

PMMA P P P Cork Wo

Butyl rubberyl ru Silicone ee elastomersome

Concreteonc

Al22O3 SiC Si S3N4

Fracture toughness - Strength

B4C

Neoprene Isoprene eather Cast irons WC WC

Soda glassa Silica glassSilicon Stone Ston Brickk ABSBS A A Epoxiesx Ep Ionomerss

Low alloy steelse

Carbon C steels Polyurethanen PA PA PA PC P PE PE PTFEFE P P PS PS P P PS P P P PPP henolice h li Ph Phhh

MFA, 04 KIc

K / σf (KIcK )cc22/ σ ff rk rk Wood Wo 100 Me eelsels PT P P P P ork Wo 100 teelsee orkrk Woo Wo eee Search region

M1= K1C/σf

chnic ceram Lead a hnical ceramics Lead alloys Leathe Ion Lead a Fo me sopr Ni o r e P a o r r P M3=σf

M2=K1C2 /σf

Figure 6.20 Materials for pressure vessels Steel, copper alloys, and aluminum alloys best satisfy the ‘‘yield-before-break’’ criterion In addition, a high yield strength allows a high

working pressure The materials in the ‘‘search areas’’ triangle are the best choice The leak-before-break criterion leads to essentially the same selection

(156)

Boiler failures used to be common place — there are even songs about it Now they are rare, though when safety margins are pared to a minimum (rockets, new aircraft designs) pressure vessels still occasionally fail This (relative) success is one of the major contributions of fracture mechanics to engineering practice

Further reading Background in fracture mechanics and safety criteria can be found in:

Brock, D (1984) Elementary Engineering Fracture Mechanics, Martinus Nijoff, Boston

Hellan, K (1985)Introduction to Fracture Mechanics, McGraw-Hill

Hertzberg, R.W (1989)Deformation and Fracture Mechanics of Engineering Materials, Wiley, New York

6.6 Materials for flywheels

6.10 Deflection-limited design with brittle polymers

6.12 Stiff, high damping materials for shaker tables

Shakers, if you live in Pennsylvania, are the members of an obscure and declining religious sect, noted for their austere wooden furniture To those who live elsewhere they are devices for vibration-testing (Figure 6.21) This second sort of shaker consists of an electromagnetic actuator driving a table, at frequencies up to 1000 Hz, to which the test-object (a space probe, an automobile, an aircraft component, or the like) is clamped The shaker applies a spectrum of vibration frequencies,f, and amplitudes,A, to the test-object to explore its response

A big table operating at high frequency dissipates a great deal of power The primary objective is to minimize this, but subject to a number of constraints itemized in Table 6.21 What materials make good shaker tables?

Table

Actuator

Oscillation

(157)

The model The powerp(Watts) consumed by a dissipative vibrating system with a sinusoidal input is

pẳC1mA2!3 6:46ị wheremis the mass of the table,Ais the amplitude of vibration,!is the frequency (rad s1) andC

1is a constant Provided the operating frequency!is significantly less than the resonant frequency of the table, thenC11 The amplitudeAand the frequency!are prescribed To minimize the power lost in shaking the table itself, we must minimize its massm We idealize the table as a disk of given radius,R Its thickness,t, is a free variable Its mass is

mẳR2t 6:47ị

where is the density of the material of which it is made The thickness influences the bending-stiffness of the table — and this is important both to prevent the table flexing too much under clamping loads, and because it determines its lowest natural vibration frequency The bending stiffness,S, is

S¼C2EI

R3

whereC2is a constant The second moment of the section,I, is proportional to t3R Thus, for a given stiffnessSand radiusR,

t¼C3 SR2

E

1=3

whereC3is another constant Inserting this into equation (6.47) we obtain mẳC3R8=3S1=3

E1=3

6:48ị The mass of the table, for a given stiffness and minimum vibration frequency, is therefore minimized by selecting materials with high values of

M1ẳ E1=3

6:49ị

Table 6.21 Design requirements for shaker tables

Function Table for vibration tester (‘‘shaker table’’) Constraints Radius,R, specified

Must be stiff enough to avoid distortion by clamping forces

Natural frequencies above maximum operating frequency (to avoid resonance)

High damping to minimize stray vibrations

Tough enough to withstand mishandling and shock Objective Minimize power consumption

Table thickness,t

(158)

There are three further requirements The first is that of high mechanical damping, measured by the loss coefficient, The second that the fracture toughness K1C of the table be sufficient to withstand mishandling and

clamping forces And the third is that the material should not cost too much

The selection Figure 6.22 shows the chart of loss coefficientplotted against modulusE The vertical line shows the constraintE30 GPa, the horizontal one, the constraint >0.001 The search region contains CFRP and a number of metals: magnesium, titanium, cast irons and steels All are possible candidates Table 6.22 compares their properties

Postscript Stiffness, high natural frequencies and damping are qualities often sought in engineering design The shaker table found its solution (in real life as well as this case study) in the choice of a cast magnesium alloy

Sometimes a solution is possible by combining materials (more on this in Chapter 13) The loss coefficient chart shows that polymers and elastomers have high damping Sheet steel panels, prone to lightly-damped vibration, can be damped by coating one surface with a polymer, a technique

L o ss co e ff ici e n t, η, at 30 oC 1000

10-3 10-2 10-1 1 10 100

10-5 10-4 10-3 10-2 10-1 10 Foams Polymers Metals Technical ceramics Composites Lead alloys W alloys Steels Ti alloys Mg alloys CFRP GFRP Al alloys Cast irons Cu alloys Zinc alloys PS PMMA Epoxies PET Cork Wood Silicone elastomers oncrete WC Al2O3

SiC

Si3N4

Loss coefficient - Modulus

Rigid polymer foams Flexible polymer foams ABS PTFE Polyurethane Butyl rubber EVA Neoprene Isoprene Leather PE Ionomers PP PC Soda glass Silica glass Non-technical ceramics Brick Stone MFA, 04

η E = 0.04 GPa Elastomers Search region η=0.001 a gl a gla alloy u all loys lloys Co E = 30 GPa

W allo s

Composites

(159)

exploited in automobiles, typewriters and machine tools Aluminum structures can be stiffened (raising natural frequencies) by bonding carbon fiber to them: an approach sometimes use in aircraft design And structures loaded in bending or torsion can be made lighter, for the same stiffness (again increasing natural frequencies), by shaping them efficiently: by attaching ribs to their underside, for instance Shaker tables — even the austere wooden tables of the Pennsylvania Shakers — exploit shape in this way

Further reading Tustin, W and Mercado, R (1984)Random Vibrations in Perspective, Tustin Institute of Technology Inc, Santa Barbara, CA, USA

Cebon, D and Ashby, M.F (1994) Materials selection for precision instruments,Meas Sci Technol.5, 296–306

6.4 Materials for table legs 6.7 Materials for springs

6.13 Insulation for short-term isothermal containers

Each member of the crew of a military aircraft carries, for emergencies, a radio beacon If forced to eject, the crew member could find himself in trying cir-cumstances — in water at 4C, for example (much of the earth’s surface is ocean with a mean temperature of roughly this) The beacon guides friendly rescue services, minimizing exposure time

But microelectronic metabolisms (like those of humans) are upset by low temperatures In the case of the beacon, it is its transmission frequency that starts to drift The design specification for the egg-shaped package containing Table 6.22 Materials for shaker tables

Material Loss coeff, M1¼E1/3/ GPa1/3/(Mg/m3)

Mg/(m)3

Comment

Mg-alloys Up to 2102 1.9 1.75 The best combination of properties

Titanium alloys

Up to 5103 1.0 4.6 Good damping but expensive

CFRP Up to 4103 3.0 1.8 Less damping than Mg-alloys,

but possible

Cast irons Up to 4103 0.7 7.8 Good damping but heavy Zinc alloys Up to 7103 0.7 5.5 Less damping than Mg-alloys,

but possible for a small table

(160)

the electronics (Figure 6.23) requires that, when the temperature of the outer surface is changed by 30C, the temperature of the inner surface should not change significantly for an hour To keep the device small, the wall thickness is limited to a thicknesswof 20 mm What is the best material for the package? A dewar system is out — it is too fragile

A foam of some sort, you might think But here is a case in which intuition leads you astray So let us formulate the design requirements (Table 6.23) and the job properly

The model We model the container as a wall of thickness w, thermal con-ductivity The heat flux q through the wall, once a steady-state has been established, is given by Fick’s first law:

q¼ dT

dx ¼

ðTiToÞ

w ð6:50Þ

whereTois the temperature of the outer surface,Tiis that of the inner one and dT/dxis the temperature gradient (Figure 6.23) The only free variable here is the thermal conductivity, The flux is minimized by choosing a wall material Table 6.23 Design requirements for short-term insulation

Function Short term thermal insulation Constraints Wall thickness must not exceedw

Objective Maximize timetbefore internal temperature changes when external temperature suddenly drops

Electronics Insulation

Wall thickness

Temp To

W

Temp Ti

(161)

with the lowest possible value of Thechart (Figure 6.24) shows that this is, indeed, a foam

But we have answered the wrong question The design brief was not to minimize theheat fluxthrough the wall, but thetimebefore the temperature of the inner wall changed appreciably When the surface temperature of a body is suddenly changed, a temperature wave, so to speak, propagates inwards The distancexit penetrates in timetis approximatelypffiffiffiffiffiffiffi2at Hereais the thermal diffusivity, defined by

aẳ

Cp

6:51ị whereis the density andCpis the specific heat (Appendix A) Equating this to the wall thicknesswgives

tw

2a ð6:52Þ

The time is maximized by choosing the smallest value of the thermal diffusivity, a, not the conductivity

T

Thheerrmmaall ddiiffffuusisivviitty,y aa ((mm22//s)//

T h e rm a l co n d u ct ivi ty , λ (W / WW mm K ) 10

10 10-7 1010-6 10-5 10-4

0.0011 0.1 10 100 1000 107 Guidelines for thermal design High volumetric specific heat Low volumetric specific heat 106 105 Vol specific heat

ρCCpp (J/m3 .K) λ a λ a1/2 Foams Polymers an elastomers Metals Technical ceramics Compositesites Lead alloys W alloys W Carbon steels

Ti alloyso

Mg alloysl

CFRP

GFRP

Al alloys

gid polymerme foamsams

Flexible polymer Fl ibl l foams Ni alloys Cu alloys Zn alloys F F PT PT PC PC Cork Wood Butyl rubber Silicone elastomerss Concretencre Al Al22OO33

SiC

Si3N4

B4C

PP Isoprene call Non-technic ceramics MFA, 04 Cast irons WC

Soda glassda Stonene Brick B Epoxies E E Stainless steels AlN A Silicon Neoprene N PMMAMM PVC PVC Rig f gh v spec d FE F N Search region ig s n s F F

M = a

Figure 6.24 Materials for short-term isothermal containers Elastomers are good; foams are not

(162)

The selection Figure 6.24 shows that the thermal diffusivities of foams are not particularly low; it is because they have so little mass, and thus heat capacity The diffusivity of heat in a solid polymer or elastomer is much lower because they have specific heats that are exceptionally large A package made of solid rubber, neoprene or isoprene, would — if of the same thickness — give the beacon a life 10 times greater than one made of (say) a polystyrene foam — though of course it would be heavier Table 6.24 summarizes the conclusions The reader can confirm, using equation (6.51), that 22 mm of a solid elastomer (a¼5108m2/s, read from Figure 6.24) will allow a time interval of more than h after an external temperature change before the internal temperature shifts much

Postscript One can better than this The trick is to exploit other ways of absorbing heat If a liquid — a low-melting wax, for instance — can be found that solidifies at a temperature equal to the minimum desired operating temperature for the transmitter (Ti), it can be used as a ‘‘latent-heat sink’’ Channels in the package are filled with the liquid; the inner temperature can only fall below the desired operating temperature when all the liquid has solidified The latent heat of solidification must be supplied to this, giving the package a large (apparent) specific heat, and thus an exceptionally low diffusivity for heat at the temperatureTi The same idea is used, in reverse, in ‘‘freezer packs’’ that solidify when placed in the freezer compartment of a refrigerator and remain cold (by melting, at 4C) when packed around warm beer cans in a portable cooler

Further reading Holman, J.P (1981)Heat Transfer, 5th edition, McGraw-Hill, New York, USA

6.14 Energy-efficient kiln walls 6.15 Materials for passive solar heating

Table 6.24 Materials for short-term thermal insulation

Material Comment

Elastomers: Butyl rubber, neoprene and isoprene are examples

Best choice for short-term insulation Commodity polymers: polyethylenes

and polypropylenes

Cheaper than elastomers, but somewhat less good for short-term insulation

Polymer foams Much less good than elastomers for short-term

insulation; best choice for long-term insulation at steady state

(163)

6.14 Energy-efficient kiln walls

The energy cost of one firing cycle of a large pottery kiln (Figure 6.25) is considerable Part is the cost of the energy that is lost by conduction through the kiln walls; it is reduced by choosing a wall material with a low con-ductivity, and by making the wall thick The rest is the cost of the energy used to raise the kiln to its operating temperature; it is reduced by choosing a wall material with a low heat capacity, and by making the wall thin Is there a material index that captures these apparently conflicting design goals? And if so, what is a good choice of material for kiln walls? The choice is based on the requirements of Table 6.25

The model When a kiln is fired, the internal temperature rises quickly from

ambient, To, to the operating temperature, Ti, where it is held for the firing time t The energy consumed in the firing time has, as we have said, two contributions The first is the heat conducted out: at steady state the heat loss by

Table 6.25 Design requirements for kiln walls

Function Thermal insulation for kiln (cyclic heating and cooling)

Constraints Maximum operating temperature 1000C

Possible limit on kiln-wall thickness for space reasons

Objective Minimize energy consumed in firing cycle

Free variables Kiln wall thickness,w

Choice of material

Temperature T Temperature To

Insulation Conductivity λ Specific heat Cp

Heater w

Figure 6.25 A kiln On firing, the kiln wall is first heated to the operating temperature, then held at this temperature A linear gradient is then expected through the kiln wall

(164)

conduction,Q1, per unit area, is given by the first law of heat flow If held for timetit is

Q1ẳ

dT

dxtẳ

TiToị

w t ð6:53Þ

Hereis the thermal conductivity, dT/dxis the temperature gradient andw is the insulation wall-thickness The second contribution is the heat absorbed by the kiln wall in raising it to Ti, and this can be considerable Per unit area, it is

Q2¼Cpw

TiTo

2

ð6:54Þ

whereCpis the specific heat of the wall material andis its density The total energy consumed per unit area is the sum of these two:

QẳQ1ỵQ2ẳ

TiỵToịt

w ỵ

CpwTiToị

2 6:55ị

A wall that is too thin loses much energy by conduction, but absorbs little energy in heating the wall itself One that is too thick does the opposite There is an optimum thickness, which we find by differentiating equation (6.54) with respect to wall thicknesswand equating the result to zero, giving:

w¼ 2t

Cp

1=2

¼ 2atị1=2 6:56ị

where aẳ/Cp is the thermal diffusivity The quantity (2at)1/2 has dimen-sions of length and is a measure of the distance heat can diffuse in time t Equation (6.56) says that the most energy-efficient kiln wall is one that only starts to get really hot on the outside as the firing cycle approaches com-pletion Substituting equation (6.55) back into equation (6.55) to eliminate w gives:

Qẳ TiToị2tị

1=2

ðCpÞ

1=2

Q is minimized by choosing a material with a low value of the quantity (Cp)1/2, that is, by maximizing

Mẳ Cpị

1=2

ẳa

1=2

6:57ị

By eliminating the wall thickness w we have lost track of it It could, for some materials, be excessively large Before accepting a candidate material we must check, by evaluating equation (6.56) how thick the wall made from it will be

The selection Figure 6.26 shows the a chart with a selection line

(165)

polymers are good, but only if the internal temperature is less than 150C. Real kilns operate near 1000C requiring materials with a maximum service temperature above this value The figure suggests brick (Table 6.26), but

T

Thheerrmmaall ddiiffffuusisivviitty,y aa ((mm22//s)//

T h e rm a l c o n d u c ti v it y , λ (W / WW mm K ) 10

10 10-7 1010-6 10-5 10-4

ρCCpp (J/m3.K)

λ a λ a1/2 Foams Polymers and elastomers Metals Technical eramics Compositesites Lead alloys W alloys W Carbon steels

Ti alloyso

Mg alloysl

CFRP

GFRP

Al alloys

Rigid polymermer

foamsams

Flexible polymer

Fl ibl l

foams Ni alloys Cu alloys Zn alloys PTFETF PC PC Cork Wood Butyl rubber Silicone elastomerss Concretencre Al Al22OO33

SiC

Si3N4

B4C

P Isoprene call Non-technic ceramics MFA, 04 Cast irons WC

Soda glassoda

Stonene Brick B Epoxies E E Stainless steels AlN A Silicon Neoprene PMMAMM PVC PVC Search region

M = a1/2/ λ 105 Technical cerami PP Neo PMMAM C cal eramic Neopr

Figure 6.26 Materials for kiln walls Low density, porous or foam-like ceramics are the best choice

Table 6.26 Materials for energy-efficient kilns

Material M¼a1/2/

(m2K/W.s1/2)

Thickness

w(mm)

Comment

Brick 103 90 The obvious choice: the lower the

density, the better the performance Special refractory bricks have values ofMas high as 3103

Concrete 5104 110 High-temperature concrete can withstand

temperatures up to 1000C

Woods 2103 60 The boiler of Stevenson’s ‘‘Rocket’’ steam

engine was insulated with wood

Solid elastomers and solid polymers

2103–3103 2103

50 Good values of material index Useful if the wall must be very thin Limited to temperatures below 150C

Polymer foam, cork

3103¼310250–100 The highest value ofM— hence their use in house insulation Limited to temperatures below 150C

(166)

here the limitation of the hard-copy charts becomes apparent: there is not enough room to show specialized materials such as refractory bricks and concretes The limitation is overcome by the computer-based methods mentioned in Chapter 5, allowing a search over 3000 rather than just 68 materials

Having chosen a material, the acceptable wall thickness is calculated from equation (6.55) It is listed, for a firing time of h (approximately 104s) in Table 6.26

Postscript It is not generally appreciated that, in an efficiently-designed kiln,

as much energy goes in heating up the kiln itself as is lost by thermal con-duction to the outside environment It is a mistake to make kiln walls too thick; a little is saved in reduced conduction-loss, but more is lost in the greater heat capacity of the kiln itself

That, too, is the reason that foams are good: they have a low thermal con-ductivityanda low heat capacity Centrally heated houses in which the heat is turned off at night suffer a cycle like that of the kiln Here (becauseTiis lower) the best choice is a polymeric foam, cork, or fiberglass (which has thermal properties like those of foams) But as this case study shows — turning the heat off at night does not save you as much as you think, because you have to supply the heat capacity of the walls in the morning

Further reading Holman, J.P (1981)Heat Transfer, 5th edition, McGraw-Hill, New York, USA Related case

studies

6.15 Materials for passive solar heating

There are a number of schemes for capturing solar energy for home heating: solar cells, liquid filled heat exchangers, and solid heat reservoirs The simplest of these is the heat-storing wall: a thick wall, the outer surface of which is heated by exposure to direct sunshine during the day, and from which heat is extracted at night by blowing air over its inner surface (Figure 6.27) An essential of such a scheme is that the time-constant for heat flow through the wall be about 12 h; then the wall first warms on the inner surface roughly 12 h after the sun first warms the outer one, giving out at night what it took in during the day We will suppose that, for architectural reasons, the wall must not be more than1

2m thick What materials maximize the thermal energy captured

(167)

The model The heat content,Q, per unit area of wall, when heated through a temperature intervalTgives the objective function

QẳwCpT 6:58ị

where w is the wall thickness, and Cp is the volumetric specific heat (the densitytimes the specific heatCp) The 12-h time constant is a constraint It is adequately estimated by the approximation used earlier for the heat-diffusion distance in time t(see Appendix A):

wẳp2at 6:59ị

whereais the thermal diffusivity Eliminating the free variablewgives

Q¼pffiffiffiffiffi2tTa1=2C

p 6:60ị

or, using the fact thataẳ/Cpwhereis the thermal conductivity,

Q¼pffiffiffiffiffi2tT

a1=2

Heat storing

wall

w Air flow

to extract heat from

wall

Fan

Figure 6.27 A heat-storing wall The sun shines on the outside during the day; heat is extracted from the inside at night The heat diffusion-time through the wall must be about 12 hours

Table 6.27 Design requirements for passive solar heating

Function Heat storing medium

Constraints Heat diffusion time through wallt12 h

Wall thickness 0.5 m

Adequate working temperatureTmax>100C

Objective Maximize thermal energy stored per unit material cost

Free variables Wall thickness,w

Choice of material

(168)

The heat capacity of the wall is maximized by choosing material with a high value of

Mẳ

a1=2 6:61ị

it is the reciprocal of the index of the previous case study The restriction on thicknesswrequires (from equation (6.59)) that

a w

2

2t

withw 0.5 m andt¼12 h (4104s), we obtain an attribute limit

a 3106m2=s ð6:62Þ

The selection Figure 6.28 shows thermal conductivity plotted against

thermal diffusivityawithM and the limit ona plotted on it It identifies the group of materials, listed in Table 6.28: they maximizeM1while meeting the

M =λ///a1/2

T

Thheerrmmaall ddiiffffuusisivviitty, y aa ((mm22//s)//

T h e rm a l c o n d u ct ivi ty , λ (W / WW mm K ) 10

10 10-7 1010-6 10-5 10-4

ρCCpp (J/m3.K)

λ a λ a1/2 Foams Polymers and elastomers Metals Technical ceramic sitesites Comp Lead alloys W alloys W arbon eels

Ti alloyso

Mg alloysl

GFRP

Al alloys

Rigid polymermer

foamsams

m Flexible polym

Fl ibl l

foams Ni alloys Cu alloys Zn alloys PTFE PTF PC PC Cork Wood Butyl rubber Silicone elastomerss Concretencre Al Al22OO33

SiC

Si3N4

B4C

PP Isoprene call Non-technic ceramics MFA, 04 Cas iron WC

Soda glassoda

Stonene Brick B Epoxies E Stainless steels AlN A Silicon Neopre PMMAMM PVC PVC Search region

a = x 10-6m2/s

pos RP mer eta Ca ste t s p R m p R e st s e t s CFR Iso eoprene l amics RP R R Neopre al ramics Neopren l amics

(169)

constraint on wall thickness Solids are good; porous materials and foams (often used in walls) are not

Postscript All this is fine, but what of cost? If this scheme is to be used for

housing, cost is an important consideration The approximate costs per unit volume, read from Figure 4.17(b), are listed in the table — it points to the selection of concrete, with stone and brick as alternatives

6.14 Energy-efficient kiln walls

6.16 Materials to minimize thermal distortion in precision devices The precision of a measuring device, like a sub-micrometer displacement gauge, is limited by its stiffness and by the dimensional change caused by temperature gradients Compensation for elastic deflection can be arranged; and corrections to cope with thermal expansion are possible too — provided the device is at a uniform temperature.Thermal gradientsare the real problem: they cause a change of shape — that is, a distortion of the device — for which compensation is not possible Sensitivity to vibration is also a problem: natural excitation introduces noise and thus imprecision into the measurement So it is permissible to allow expansion in precision instrument design, provided distortion does not occur (Chetwynd, 1987) Elastic deflection is allowed, provided natural vibration frequencies are high

What, then, are good materials for precision devices? Table 6.29 lists the requirements

The model Figure 6.29 shows, schematically, such a device: it consists for a

force loop, an actuator and a sensor We aim to choose a material for the force loop It will, in general, support heat sources: the fingers of the operator of the

Table 6.28 Materials for passive solar heat-storage

Material M1¼/a1/2

(W.s1/2/m2.K)

Approx cost

$/m3

Comment

Concrete 2.2103 200 The best choice — good performance at

minimum cost

Stone 3.5103 1400 Better performance than concrete because

specific heat is greater, but more expensive

Brick 103 1400 Less good than concrete

Glass 1.6103 10,000 Useful — part of the wall could be glass

Titanium 4.6103 200,000 An unexpected, but valid, selection Expensive

(170)

device in the figure, or, more usually, electrical components that generate heat The relevant material index is found by considering the simple case of one-dimensional heat flow through a rod insulated except at its ends, one of which is at ambient and the other connected to the heat source In the steady state, Fourier’s law is

qẳ dT

dx 6:63ị

whereqis heat input per unit area,is the thermal conductivity and dT/dxis the resulting temperature gradient The strain is related to temperature by

"ẳToTị 6:64ị

where is the thermal conductivity andTois ambient temperature The dis-tortion is proportional to the gradient of the strain:

d" dx¼

dT

dx ¼

q ð6:65Þ

Thus for a given geometry and heat flow, the distortion dE/dxis minimized by selecting materials with large values of the index

M1¼

Actuator

and sensor

Force loop

Probe

Figure 6.29 A schematic of a precision measuring device Super-accurate dimension-sensing devices include the atomic-force microscope and the scanning tunneling microscope

Table 6.29 Design requirements for precision devices

Function Force loop (frame) for precision device

Constraints Must tolerate heat flux

Must tolerate vibration

Objective Maximize positional accuracy (minimize distortion)

(171)

The other problem is vibration The sensitivity to external excitation is minimized by making the natural frequencies of the device as high as possible The flexural vibrations have the lowest frequencies; they are proportional to

M2¼

E1=2

A high value of this index will minimize the problem Finally, of course, the device must not cost too much

The selection Figure 6.30 shows the expansion coefficient, , plotted

against the thermal conductivity, Contours show constant values of the quantity/ A search region is isolated by the line/¼107W/m, giving the short list of Table 6.30 Values of M2¼E1/2/read from the Echart of

Figure 4.3 are included in the table Among metals, copper, tungsten and the special nickel alloy Invar have the best values of M1 but are disadvantaged by having high densities and thus poor values of M2 The best choice is silicon, available in large sections, with high purity Silicon carbide is an alternative

T

Thheerrmmaall coconndduuctctiivviitty,y,λλ((WW//WWW mm.K)

0 0011

T h e rm a ll e x p a n i si o n, α ((µ t st iin /K ) 0.11 1

0.1 1010 100 1000

1 10 100 1000 = 10 = =

Large thermal strain mismatch

Small thermal strain mismatch λ

αα (W/m)

λ

αα (W/m

1044 105

106 106 107 =107 104 105 Foams Polymers and elastomers Metals Techncial ceramics Composites

Natural materm terialsterrrias

Lead alloysead alloys

Lead L Lead Le W alloys Steelss Ti alloys oys oys Mg alloy CFRP GFRP G Al alloys A A Rigid polymer Rig foams Flexible polymer foams

Ni alloysi ao

Cu alloys

Zn alloysn

PA PA PMMAM P P A PC PET Wood Butyl rubbery Silicone elastomersme Concrete C WC

Al2OO3 SiC

3

3NN4

T-expansion - T-conductivity

Pb alloys Stainlessn steelse Sil ss ss Silicon AlN Soda glasss Neoopreneo PEE Epoxies Ep ABS AB E

MFA, 044

Invar ma

m

Search region

m)=1=

10 s Mg alloy A Si3N Silica glass =1 107 loysoy Al A 3NN assss =1 3N ass

M =λ/α

Figure 6.30 Materials for precision measuring devices Metals are less good than ceramics because they have lower vibration frequencies Silicon may be the best choice

(172)

Postscript Nano-scale measuring and imaging systems present the problem analyzed here The atomic-force microscope and the scanning-tunneling microscope both rely on a probe, supported on a force loop, typically with a piezo-electric actuator and electronics to sense the proximity of the probe to the test surface Closer to home, the mechanism of a video recorder and that of a hard disk drive qualify as precision instruments; both have a sensor (the read head) attached, with associated electronics, to a force loop The materials identified in this case study are the best choice for force loop

Further reading Chetwynd, D.G (1987)Precision Engineering,9(1),

Cebon, D and Ashby, M.F (1994)Meas Sci Technol.,5, 296

6.3 Mirrors for large telescopes

6.17 Nylon bearings for ships’ rudders

Rudder bearings of ships (Figure 6.31 and Table 6.31) operate under the most unpleasant conditions The sliding speed is low, but the bearing pressure is high and adequate lubrication is often difficult to maintain The rudder lies in the wake of the propeller, which generates severe vibration and consequent fretting Sand and wear debris tend to get trapped between the bearing surfaces Add to this the environment — aerated salt water — and you can see that bearing design is something of a challenge

Ship bearings are traditionally made of bronze The wear resistance of bronzes is good, and the maximum bearing pressure (important here) is high

Table 6.30 Materials to minimize thermal distortion

Material M1¼/

(W/m)

M2¼E1/2/

(GPa1/2/(Mg/m3))

Comment

Silicon 6107 5.2 ExcellentM1andM2

Silicon carbide 3107 6.4 ExcellentM1andM2but more

difficult to shape than silicon

Copper 2107 1.3 High density gives poor value of

M2

Tungsten 3107 1.1 Better than copper, silver or gold,

but less good than silicon or SiC

Aluminum alloys 107 3.3 The cheapest and most easily

(173)

But, in sea water, galvanic cells are set up between the bronze and any other metal to which it is attached by a conducting path (no matter how remote), and in a ship such connections are inevitable So galvanic corrosion, as well as abrasion by sand, is a problem Is there a better choice than bronze?

The model We assume (reasonably) that the bearingforce, F, is fixed by the

design of the ship The bearingpressure,P, can be controlled by changing the areaAof the bearing surface:

P/F

A

This means that we are free to choose a material with a lower maximum bearing pressure provided the length of the bearing itself is increased to com-pensate With this thought in mind, we seek a bearing material that will not corrode in salt water and can function without full lubrication

Head Carrier

Stock Bush

Pintle Bush

Rudder

Figure 6.31 A ship’s rudder and its bearings

Table 6.31 Design requirements for rudder bearings

Function Sliding bearing

Constraints Wear resistant with water lubrication

Resist corrosion in sea water High damping desirable

Objective Maximize life, meaning minimize wear rate

Bearing diameter and length

(174)

The selection Figure 6.32 shows the chart of wear-rate constant, ka, and hardness,H The wear-rate,W, is given by equation (4.26), which, repeated, is

¼kaP¼C

P

Pmax

kaH

whereCis a constant,Pis the bearing pressure,Pmaxthe maximum allowable bearing pressure for the material, andH is its hardness If the bearing is not re-sized when a new material is used, the bearing pressurePis unchanged and the material with the lowest wear-rate is simply that with the smallest value of the quantity

M1¼ka

Bronze performs well, but filled thermoplastics are nearly as good and have superior corrosion resistance in salt water If, on the other hand, the bearing is re-sized so that it operates at a set fraction ofPmax(0.5, say), the material with the lowest wear-rate is that with the smallest value of

M2¼kaH

Here polymers are clearly superior Table 6.32 summarizes the conclusions Haarrddnneess, H ss H ((MMPa)

W e aa rr-rraa ttee coco nn stst aa nn tt k , ktt aa ((11 //(( MM PP a ))

100 100 11000000 10,000 100,000

100-1111

10-10 10 -9 10 -8 10 -7 10 -6 10-5 10-4 10-6 10-7 10-5 10-4

10-3 Dimensionless

wear contant K = kkk HaH

Polymers and elastomers Metals Technical ceramics Stainless steels Al alloys

Cu alloysys

PMMAM

Al2O3 SiC Wear rate - Hardness

Cast irons

WC

Silica glass Silica

Low alloy steels Tool steels Low carbon steels PA PC PE PTFE PP MFA, 04

Medium carbonm steels s

High carbon steels g Bronze Filled thermoplastics Unfilled PE Unfilled thermoplastics Search region

M2= kaH PE

p PE p 10

M1= ka

(175)

Postscript Recently, at least one manufacturer of marine bearings has started to supply cast Nylon-6 bearings for large ship rudders The makers claim just the advantages we would expect from this case study:

(a) wear and abrasion resistance with water lubrication is improved;

(b) deliberate lubrication is unnecessary;

(c) corrosion resistance is excellent;

(d) the elastic and damping properties of Nylon-6 protect the rudder from shocks (see the damping/modulus chart);

(e) there is no fretting;

(f) the material is easy to handle and install, and is inexpensive to machine Figure 6.32 suggests that a filled polymer or composite might be even better Carbon–fiber filled nylon has better wear resistance than unfilled nylon, but it is less tough and flexible, and it does not damp vibration as effectively As in all such problems, the best material is the one that comes closest to meeting all the demands made on it, not just the primary design criterion (in this case, wear resistance) The suggestion of the chart is a useful one, worth a try It would take sea-tests to tell whether it should be adopted

6.18 Materials for heat exchangers

This and the next case study illustrate the output of the CES software described in Sections 5.5

Heat exchangers take heat from one fluid and pass it to a second (Figure 6.33) The fire-tube array of a steam engine is a heat exchanger, taking heat from the hot combustion gases of the firebox and transmitting it to the water in the boiler The network of finned tubes in an air conditioner is a heat exchanger, taking heat from the air of the room and dumping it into the working fluid of the conditioner A key element in all heat exchangers is the tube wall or membrane that separates the two fluids It is required to transmit heat, and there is frequently a pressure difference across it, which can be large

Table 6.32 Materials for rudder bearings

Material Comment

PTFE, polyethylenes polypropylenes, nylon

Low friction and good wear resistance at low bearing pressures

Glass-reinforced PTFE, filled polyethylenes and polypropylenes

Excellent wear and corrosion resistance in sea water A viable alternative to bronze if bearing pressures are not too large

Silicon carbide SiC, alumina Al2O3, tungsten carbide WC

(176)

What are the best materials for making heat exchangers? Or, to be specific, what are the best materials for a conduction-limited exchanger with substantial pressure difference between the two fluids, one of them containing chloride ions (sea water) Table 6.33 summarizes these requirements

The model First, a little background on heat flow Heat transfer from one

fluid, through a membrane to a second fluid, involvesconvectivetransfer from fluid into the tube wall,conductionthrough the wall, andconvectionagain to transfer it into fluid The heat flux into the tube wall by convection (W/m2) is described by the heat transfer equation:

qẳh1T1 6:66ị

in whichh1is the heat transfer coefficient andT1is the temperature drop across the surface from fluid into the wall Conduction is described by the conduction (or Fourier) equation, which, for one-dimensional heat-flow takes the form:

q¼T

t ð6:67Þ

Fluid

Pressure p2,Temperature T2

Pressure p1, Temperature T1

2r

t ∆T = T1 - T2 ∆p = p1 - p2

Figure 6.33 A heat exchanger There is a pressure differencepand a temperature differenceTacross the tube wall that also must resist attack by chloride ions

Table 6.33 Design requirements for a heat exchanger

Function Heat exchanger

Constraints Support pressure difference,p

Withstand chloride ions

Operating temperature up to 150C

Modest cost

Objective Maximize heat flow per unit area (minimum volume exchanger) or

Maximize heat flow per unit mass (minimum mass exchanger)

Free variables Tube-wall thickness,t

(177)

where is the thermal conductivity of the wall (thickness t) and T is the temperature difference across it It is helpful to think of the thermal

resistance at surface as 1/h1; that of surface is 1/h2; and that of the

wall itself ist/ Then continuity of heat flux requires that the total resistance 1/Uis

1

U¼

1 h1

ỵt

ỵ

1 h2

ð6:68Þ

whereUis called the ‘‘total heat transfer coefficient’’ The heat flux from fluid to fluid is then given by

qẳUT1T2ị 6:69ị

where (T1T2) is the difference in temperature between the two working fluids

When one of the fluids is a gas — as in an air conditioner — convective heat transfer at the tube surfaces contributes most of the resistance; then fins are used to increase the surface area across which heat can be transferred But when both working fluids are liquid, convective heat transfer is rapid and conduction through the wall dominates the thermal resistance; 1/h1and 1/h2 are negligible compared witht/ In this case, simple tube or plate elements are used, making their wall as thin as possible to minimizet/ We will consider the second case: conduction-limited heat transfer, where the heat flow is ade-quately described by equation (6.63)

Consider, then, a heat exchanger withntubes of lengthL, each of radiusrand wall thicknesst Our aim is to select a material to maximize the total heat flow:

QẳqAẳA

t T 6:70ị

whereA¼2rLnis the total surface are of tubing

This is the objective function The constraint is that the wall thickness must be sufficient to support the pressurepbetween the inside and outside, as in Figure 6.33 This requires that the stress in the wall remain below the elastic limit, y, of the material of which the tube is made (multiplied by a safety factor — which we can leave out):

ẳpr

t < y 6:71ị

This constrains the minimum value oft Eliminatingtbetween equations (6.70) and (6.71) gives

QẳAT

rp yị 6:72ị

The heat flow per unit area of tube wall,Q/A, is maximized by maximizing

M1ẳy 6:73ị

(178)

Four further considerations enter the selection It is essential to choose a material that can withstand corrosion in the working fluids, which we take to be water containing chloride ions (sea water) Cost, too, will be of concern The maximum operating temperature must be adequate and the materials must have sufficient ductility to be drawn to tube or rolled to sheet Cost, too, will be of concern

The selection A preliminary search (not shown) for materials with large

values ofM1, using the CES Level 1/2 database , suggestscopper alloysas one possibility We therefore turn to the Level database for more help The first selection stage applies limits of 150C on maximum service temperature, 30 percent on elongation, a material cost of less than $4/kg and requires a rating of ‘‘very good’’ resistance to sea water The second stage (Figure 6.34) is a chart ofyversusenablingM1¼yto be maximized The materials with largeM1are listed in Table 6.34

Postscript Conduction may limit heat flow in theory, but unspeakable things

go on inside heat exchangers Sea water — often one of the working fluids — seethes with bio-fouling organisms that attach themselves to tube walls and thrive there, like barnacles on a boat, creating a layer of high thermal resistance

Thermal conductivityλ(W/WW m.K)

20 50 100 200 500

50 100 500 1000 2000

200

E

la

s

ti

c

L

im

it

σy

(M

P

a

)

Cu-Cr Cu-Ni-Fe-AlAA bronze UNS C63020e

Mn-bronze, C86300e 7% Phosphor bronze UNS C51900

630 nz

5% Phosphor bronze

0 ho

95/5 AlAA -bronze UNS C60800e

Brass UNS C44300)NS Mn-bronze Cu-Zn-AlAA -Mn

B C

Cu-Co-Be UNS C82000e U Cu-Cr-ZrC

Brass UNS C26800ass UNS Brass UNS C28000S Brass UNS

Brass UNS C23000S B s UNS

70/00 30 brass UNS C43600UU 18% Nickel silver UNS C77000)e

Gunmetal UNS C83600N 80/00 2// Cu-Ni UNS C71000UU

18% Nickel SilverUNS C75200ee Phosphor bronze UNS C90710e U

Al A

A -bronze UNS C63000NS C6

93/33 AlAA -bronzebb

Search region Copper alloys

M =σfλ

Figure 6.34 A chart of yield strength (elastic limit)yagainst thermal conductivity,, showing the

(179)

impeding fluid flow A search for supporting information reveals that some materials are more resistant to biofouling than others; copper-nickel alloys are particularly good, probably because the organisms dislike copper salts, even in very low concentrations Otherwise the problem must be tackled by adding chemical inhibitors to the fluids, or by scraping — the traditional winter pas-time of boat owners

It is sometimes important to minimize the weight of heat exchangers Repeating the calculation to seek materials the maximum value ofQ/m(where mis the mass of the tubes) gives, instead ofM1, the index

M2¼

y2

ð6:74Þ

where is the density of the material of which the tubes are made (The strengthyis now raised to the power of because the weight depends on wall thickness as well as density, and wall thickness varies as1/y(equation 6.71).) Similarly, the cheapest heat exchangers are those made of the material with the greatest value of

M3ẳ

y2

Cm

6:75ị

whereCmis the cost per kg of the material In both cases aluminum alloys score highly because they are both light and cheap The selections are not shown but can readily be explored using the CES system

Further reading Holman, J.P (1981)Heat Transfer, 5th edition, McGraw-Hill, New York, USA Related case

studies

Table 6.34 Materials for heat exchangers

Material Comment

Brasses Liable to dezincification

Phosphor bronzes Cheap, but not as corrosion resistant as

aluminum-bronzes

Aluminum-bronzes, wrought An economical and practical choice

(180)

6.19 Materials for radomes

This and the previous case study illustrate the output of the CES software described in Sections 5.6

When the BBC4 want to catch you watching television without a license, they park outside your house an unmarked van equipped to detect high-frequency radiation The vehicle looks normal enough, but it differs from the norm alone in one important respect: the body-skin is not made of pressed steel, but of a material transparent to microwaves The requirements of the body are much the same as those for the protective dome enclosing the delicate detectors that pick up high frequency signals from space; or those that protect the radar equipment in ships, aircraft, and spacecraft What are the best materials to make them?

The function of a radome is to shield a microwave antenna from the adverse effects of the environment, while having as little effect as possible on the electrical performance When trying to detect incoming signals that are weak to begin with, even a small attenuation of the signal as it passes through the radome decreases the sensitivity of the system Yet the radome must withstand structural loads, loads caused by pressure difference between the inside and outside of the dome, and — in the case of supersonic flight — high tempera-tures Table 6.35 summarizes the design requirements

The model Figure 6.35 shows an idealized radome It is a hemispherical skin

of microwave-transparent material of radius Rand thicknesst, supporting a pressure-differencepbetween its inner and outer surfaces The two critical material properties in determining radome performance are the dielectric constant, E, and the electric loss tangent tan Losses are of two types:

reflectionandabsorption The fraction of the signal that is reflected is related to

the dielectric constantEand the higher the frequency, the higher the reflected fraction Air has a dielectric constant of 1; a radome with the same dielectric constant, if it were possible, would not reflect any radiation (‘‘stealth’’ tech-nology seeks to achieve this)

The second, and often more important loss is that due to absorption as the signal passes through the skin of the radome When an electro-magnetic wave of frequency f (cycles/s) passes through a dielectric with loss tangent tan , the fractionalpower lossin passing through a thickness dtis

du

u ¼

fA2"

0

2 ð"tan Þdt ð6:76Þ

4

(181)

whereAis the electric amplitude of the wave andE0the permitivity of vacuum For a thin shell (thicknesst) the loss per unit area is thus

U

U ¼

fA2"

0t

2 ð"tan Þ ð6:77Þ

This is the quantity we wish to minimize — the objective function — and this is achieved by making the skin as thin as possible But the need to support a pressure differencepimposes a constraint The pressure difference creates a stress

¼pR

2t ð6:78Þ

in the skin If it is to support p, this stress must be less than the failure stress f of the material of which it is made, imposing a constraint on the thickness:

tpR

2f

Substituting this into the equation (6.77) gives

U

U ¼

fA2"

0pR

4

"tan

f

ð6:79Þ

2 R

t

∆p Radome

Figure 6.35 A radome It must be transparent to microwaves yet support wind loads and, in many application, a pressure difference

Table 6.35 Design requirements for a radome

Function Radome

Constraints Support pressure differencep

Tolerate temperature up toTmax

Objective Minimize dielectric loss in transmission of microwaves

Free variables Thickness of skin,t

Choice of material

(182)

E

la

st

ic

l

im

it

σy

(M

P

a

)

[Dielectric Constant]×[Power Factor]

100-5-5 10-4 10-3 10-2 10-1

100 100 1000

(a)

PTFE PE

PFA (Unfilled) Polysyy tyryy ene PS (Heat Resistant) PPS (10-20% glass fiber)

PPS (50% glass fiber) Polyayy mideimide

PAIAA (30% Glass Fiber)

Polyeyy ster (Glass Fiber, WoWW ven Fabric)

PEI (30% Glass Fiber)

Search region

Polymers M =σf/ εtanδ

E

la

st

ic li

m

it

σyy

(M

P

a

)

[Dielectric Constant]×[Power Factor]

10-5 10-4 10-33 10-22 10-1

100

1

1000

Search region

Ceramics

Silicaaaa

Titanium Silicatettte

Silicon Nitrideee

Zirconia (Y2O3 stabilissee

Zirconiaaaa

Berylyy liaa

Silicon Carbiddde

Zirconia (Y-TZP)(HHHIP)

All A

A ummmina (99.5)(finegrain)

Al A

A umina (pressed and sinterrredd))

Berylyy liaa

Al A

A umina (90% denssse))

Borosilicate glassss

Soda Limee

G

Glass cerammic

=σf / εtanδ (b)

Figure 6.36 (a) The elastic limit,f, plotted against the power factor,Etan , using the Level CES

database Here the selection is limited to polymers and polymer–matrix composites

(b) The same chart as Figure 6.36(a), imposing the requirement thatTmax>300C

(183)

The power loss is minimized by maximizing the index

M1ẳ

f

"tan 6:80ị

There are further constraints Resistance to abrasion (impact of small particles) scales with hardness, which in turn scales with yield or fracture strength, f, so — when abrasion is important — one might seek also to maximize

M2¼f

Toughness may also be a consideration In supersonic flight heating becomes important; then a constraint on maximum service temperature applies also

The selection A preliminary survey using the Level 1/2 database shows that

polymers have attractive values ofM1, but have poor values ofM2and can only be used at and near ambient temperature (Figure 3.36) Certain ceramics, too, are good when measured byM1and are stable to high temperatures For help we turn to the Level database Appropriate charts are shown in Figure 6.36(a) and (b) The axes are f and E tan Both have a selection line of slope 1, corresponding toM1 The first uses data for polymers and polymer composites In the second a constraint of maximum service temperature>300C has been imposed; only ceramics survive The selection is summarized in Table 6.36 The materials of the first row — teflon, (PTFE) polyethylene, and poly-propylene — maximizeM1 If greater strength or impact resistance is required, the fiber-reinforced polymers of the second row are the best choice When, additionally, high temperatures are involved, the ceramics listed in the third row become candidates

Postscript What are real radomes made of? Among polymers, PTFE and

polycarbonate are the commonest Both are very flexible Where structural rigidity is required (as in the BBC van) GFRP (epoxy or polyester reinforced with woven glass cloth) are used, though with some loss of performance

Table 6.36 Materials for radomes

Material Comment

PTFE, polyethylenes,

polypropylenes, polystyrene and polyphenylene sulfide (PPS)

Minimum dielectric loss, but limited to near room temperature

Glass-reinforced polyester, PTFE, polyethylenes and polypropylenes, polyamideimide

Slightly greater loss, but greater strength and temperature resistance

Silica, alumina, beryllia, silicon carbide

The choice for re-entry vehicles and rockets where heating is great

(184)

When performance is at a premium, glass-reinforced PTFE is used instead For skin-heating up to 300C, polymides meet the requirements; beyond that temperature it has to be ceramics Silica (SiO2), alumina (Al2O3), beryllia (BeO) and silicon nitride (Si3N4) are all employed The choices we have identified are all there

Further reading Huddleston, G.K and Bassett, H.L (1993) in Johnson, R.C and Jasik, H (eds),

Antenna Engineering Handbook, 2nd edition McGraw-Hill, New York, Chapter 44

Lewis, C.F (1988) Materials keep a low profile,Mech Eng., June, 37–41

The case studies of this chapter illustrate how the choice of material is narrowed from the initial, broad, menu to a small subset that can be tried, tested, and examined further Most designs make certain non-negotiable demands on a material: it must withstand a temperature greater thanT, it must resist corrosive fluidF, and so forth These constraints narrow the choice to a few broad classes of material The choice is narrowed further by seeking the combination of properties that maximize performance (combinations like E1/2/) or maximize safety (combinations likeK1C/f) or conduction or

insu-lation (likea1/2/) These, plus economics, isolate a small subset of materials for further consideration

The final choice between these will depend on more detailed information on their properties, considerations of manufacture, economics and aesthetics These are discussed in the chapters that follow

6.21 Further reading

The texts listed below give detailed case studies of materials selection They generally assume that a short-list of candidates is already known and argue their relative merits, rather than starting with a clean slate, as we here

Callister, W.D (2003)Materials Science and Engineering, An Introduction, 6th edition,

John Wiley, New York, USA ISBN 0-471-13576-3

Charles, J.A., Crane, F.A.A and Furness, J.A.G (1997) Selection and Use of

Engineering Materials, 3rd edition, Butterworth-Heinemann, Oxford, UK ISBN

(185)

Dieter, G.E (1991) Engineering Design, a Materials and Processing Approach, 2nd

edition, McGraw-Hill, New York, USA ISBN 0-07-100829-2 (A well-balanced and

respected text focusing on the place of materials and processing in technical design.)

Farag, M.M (1989) Selection of Materials and Manufacturing Processes for

Engineering Design, Prentice-Hall, Englewood Cliffs, NJ, USA ISBN 0-13-575192-6 (A materials-science approach to the selection of materials.)

Lewis, G (1990)Selection of Engineering Materials, Prentice-Hall, Englewood Cliffs,

NJ, USA ISBN 0-13-802190-2 (A text on material selection for technical design,

based largely on case studies.)

(186)

Cut Feed

Punch

Die

Die Die Blank Pressure

Chapter Contents

7.2 Classifying processes 177

7.3 The processes: shaping, joining, and finishing 180

7.4 Systematic process selection 195

7.5 Ranking: process cost 202

7.6 Computer-aided process selection 209

7.7 Supporting information 215

(187)

Aprocessis a method of shaping, joining, or finishing a material.Sand casting, injection molding, fusion welding,andelectro-polishingare all processes; there are hundreds of them It is important to choose the right process-route at an early stage in the design before the cost-penalty of making changes becomes large The choice, for a given component, depends on the material of which it is to be made, on its size, shape and precision, and on how many are to be made — in short, on thedesign requirements A change in design requirements may demand a change in process route

Each process is characterized by a set of attributes: the materials it can handle, the shapes it can make and their precision, complexity, and size The intimate details of processes make tedious reading, but have to be faced: we describe them briefly in Section 7.3, using process selection charts to cap-ture their attributes

Process selection— finding the best match between process attributes and design requirements — is the subject of Sections 7.4 and 7.5 In using the methods developed there, one should not forget that material, shape, and processing interact (Figure 7.1) Material properties and shape limit the choice of process: ductile materials can be forged, rolled, and drawn; those that are brittle must be shaped in other ways Materials that melt at modest

Function

Material Shape

Process

Attributes: material, shape and size, minimum section thickness

tolerance and roughness, minimum section

batch size capital cost

Figure 7.1 Processing selection depends on material and shape The ‘‘process attributes’’ are used as criteria for selection

(188)

temperatures to low-viscosity liquids can be cast; those that not have to be processed by other routes Shape, too, can influence the choice of process Slender shapes can be made easily by rolling or drawing but not by casting Hollow shapes cannot be made by forging, but they can by casting or molding Conversely, processing affects properties Rolling and forging change the hardness and texture of metals, and align the inclusions they contain, enhancing strength, and ductility Composites only acquire their properties during processing; before, they are just a soup of polymer and a sheaf of fibers Like the other aspects of design, process selection is an iterative procedure The first iteration gives one or more possible processes-routes The design must then be re-thought to adapt it, as far as possible, to ease of manufacture by the most promising route The final choice is based on a comparison of process-cost, requiring the use of cost models developed in Section 7.6, and on sup-porting information: case histories, documented experience and examples of process-routes used for related products (Section 7.7) Supporting information helps in another way: that of dealing with the coupling between process and material properties Processes influence properties, sometimes in a desired way (e.g heat treatment) sometimes not (uncontrolled casting defects, for instance) This coupling cannot be described by simple processes attributes, but requires empirical characterization or process modeling

The chapter ends, as always, with a summary and annotated recommen-dations for further reading

7.2 Classifying processes

Manufacturing processes can be classified under the headings shown in Figure 7.2 Primary processescreateshapes The first row lists seven primary forming processes: casting, molding, deformation, powder methods, methods for forming composites, special methods, and rapid prototyping Secondary processes modify shapes or properties; here they are shown as ‘‘machining’’, which adds features to an already shaped body, and ‘‘heat treatment, which enhances surface or bulk properties Below these comesjoining, and, finally, finishing

The merit of Figure 7.2 is as a flow chart: a progression through a manu-facturing route It should not be treated too literally: the order of the steps can be varied to suit the needs of the design The point it makes is that there are three broad process families: those of shaping, joining, and finishing The attributes of one family differ so greatly from those of another that, in assembling and structuring data for them, they must be treated separately

(189)

Raw materials Casting methods: Sand Die Investment Molding methods: Injection Compression Blow molding Deformation methods: Rolling Forging Drawing Powder methods: Sintering HIPing Slip casting Special methods: Rapid prototype Lay-up Electro-form Welding:

MIG, TIG, solder, hot gas and bar

Adhesives: Flexible, rigid Fasteners: Rivet, bolt, stable, sew Machining:

Cut, turn, plane drill, grind Heat treatment: Quench, temper, age-harden Polish: Electro-polish, lap, burnish Coating: Electro-plate Anodize, spray Paint/Print:

Enamel, pad print silk screen Texture: Roll, laser electro-texture SHAPING FINISHING JOINING

Figure 7.2 The classes of process The first row contains the primary shaping processes; below lie the secondary processes of machining and heat treatment, followed by the families of joining and finishing processes

Process Joining Shaping Finishing Casting Deformation Molding Composite Powder Prototyping Compression Rotation Transfer Injection Foam Extrusion Resin casting Blow molding Thermoforming

A process record

Density Mechanical props Thermal props Electrical props Optical props Corrosion props Supporting information specific general Material Shape Size range Minimum section Tolerance Roughness Supporting information

Family Class Member Attributes

Kingdom

Minimum batch size Cost model

Figure 7.3 The taxonomy of the kingdom of process with part of theshapingfamily expanded Each member is characterized by a set of attributes Process selection involves matching these to the requirements of the design

(190)

kingdom has three families: shaping, joining, and finishing In this figure, the shaping family is expanded to show classes: casting, deformation, molding, etc One of these — molding — is again expanded to show its members: rotation molding, blow molding, injection molding, and so forth Each of these have certain attributes: the materials it can handle, the shapes it can make, their size, precision, and an optimum batch size (the number of units that it can make economically) This is the information that you would find in a record for a shaping-process in a selection database

The other two families are partly expanded in Figure 7.4 There are three broad joining classes: adhesives, welding, and fasteners In this figure one of them — welding — is expanded to show its members As before each member has attributes The first is the material or materials that the process can join After that the attribute-list differs from that for shaping Here the geometry of the joint and the way it will be loaded are important, as are requirements that the joint can, or cannot, be disassembled, be watertight, be electrically con-ducting and the like

The lower part of the figure expands the family of finishing Some of the classes it contains are shown; one — coating — is expanded to show some of its members As with joining, the material to be coated is an important attribute but the others again differ Most important is the purpose of the treatment, followed by properties of the coating itself

Process records

Heat treat Paint/print Coat Polish Texture

Electroplate Anodize Powder coat Metalize

Material

Purpose of treatment Coating thickness Surface hardness Relative cost

Supporting information Material

Purpose of treatment Coating thickness Surface hardness Relative cost

Supporting information

Adhesives Welding Fasteners

Braze

Gas Arc e-beam Hot gas

Material Joint geometry Size Range Section thickness Relative cost

Supporting information Material

Joint geometry Size Range Section thickness Relative cost

Supporting information

Class Member Attributes

Kingdom

Finishing Joining

Family

Shaping Process

Solder

Hot bar

(191)

With this background we can embark on our lightning tour of processes It will be kept as concise as possible; details can be found in the numerous books listed in Section 7.9

7.3 The processes: shaping, joining, and finishing

Shaping processes

In casting (Figure 7.5), a liquid is poured or forced into a mold where it solidifies by cooling Casting is distinguished from molding, which comes next, by the low viscosity of the liquid: it fills the mold by flow under its own weight (as in gravity sand and investment casting) or under a modest pressure (as in die casting and pressure sand casting) Sand molds for one-off castings are cheap; metal dies for die-casting large batches can be expensive Between these extremes lie a number of other casting methods: shell, investment, plaster-mold and so forth

Cast shapes must be designed for easy flow of liquid to all parts of the mold, and for progressive solidification that does not trap pockets of liquid in a solid shell, giving shrinkage cavities Whenever possible, section thicknesses are made uniform (the thickness of adjoining sections should not differ by more than a factor of 2) The shape is designed so that the pattern and the finished casting can be removed from the mold Keyed-in shapes are avoided because they lead to ‘‘hot tearing’’ ( a tensile creep-fracture) as the solid cools and shrinks The tolerance and surface finish of a casting vary from poor for sand-casting to excellent for precision die-sand-castings; they are quantified in Section 7.5 When metal is poured into a mold, the flow is turbulent, trapping surface oxide and debris within the casting, giving casting defects These are avoided by filling the mold from below in such a way that flow is laminar, driven by a vacuum or gas pressure as shown in Figure 7.4

Molding (Figure 7.6) Molding is casting, adapted to materials that are very viscous when molten, particularly thermoplastics and glasses The hot, viscous fluid is pressed or injected into a die under considerable pressure, where it cools and solidifies The die must withstand repeated application of pressure, tem-perature and the wear involved in separating and removing the part, and therefore is expensive Elaborate shapes can be molded, but at the penalty of complexity in die shape and in the way it separates to allow removal The molds for thermo-forming, by contrast, are cheap Variants of the process use gas pressure or vacuum to mold form a heated polymer sheet onto a single-part mold Blow-molding, too, uses a gas pressure to expand a polymer or glass blank into a split outer-die It is a rapid, low-cost process well suited for mass-production of cheap parts like milk bottles Polymers, like metals, can be

(192)

extruded; virtually all rods, tubes and other prismatic sections are made in this way

Deformation processing (Figure 7.7) This process can be hot, warm or cold — cold, that is, relative to the melting point of the Tm material being

Mould

cavity Runner

Sand mold

Parting line

Core Crucible

Sand casting

Wax patterns Vacuum

Refractory

slurry Metal

Investment casting

Ejector pins

Die cavity Crucible

Plunger

Fixed die Movingdie

Die casting

Heat Cores

Gas pressure Zircon sand

with binder

Low pressure casting

(193)

processed Extrusion, hot forging and hot rolling (T>0.55Tm) have much in common with molding, though the material is a true solid not a viscous liquid The high temperature lowers the yield strength and allows simultaneous recrystallization, both of which lower the forming pressures Warm working

Pressure screw Hopper Extruded

product

Heating jacket

Polymer extrusion

Split

die Blank Gas pressure

Blow-molding

Heater Screw

Granular polymer Mold

Nozzle Cylinder

Injection-molding

Vents

Vacuum Vacuum

Vacuum Plug Sheet

Heater Heater

Sheet Heater

(a) Vacuum forming

(c) Pressure forming

(b) Drape forming

(d) Plug-assisted

Thermo-forming

Figure 7.6 Molding processes Ininjection-molding, a granular polymer (or filled polymer) is heated, compressed and sheared by a screw feeder, forcing it into the mold cavity In

blow-molding, a tubular blank of hot polymer or glass is expanded by gas pressure against the inner wall of a split die Inpolymer extrusion, shaped sections are formed by extrusion through a shaped die Inthermo-forming, a sheet of thermoplastic is heated and deformed into a female die by vacuum or gas pressure

(194)

(0.35Tm<T<0.55Tm) allows recovery but not recrystallization Cold forging, rolling, and drawing (T<0.35Tm) exploit work hardening to increase the strength of the final product, but at the penalty of higher forming pressures

Forged parts are designed to avoid rapid changes in thickness and sharp radii of curvature since both require large local strains that can cause the material to Upper die

Lower die

Work piece

Forging Rolling

Ram

Ram Die

Die

Billet

Billet Direct extrusion

Indirect extrusion

Extruded product

Extrusion

Final shape

Shaped blank

Original blank

Pin Headstock

Tool rest

Tailstock

Tool

Spinning

Figure 7.7 Deformation processes Inforging, a slug of metal is shaped between two dies held in the jaws of a press Inrolling, a billet or bar is reduced in section by compressive deformation between the rolls Inextrusion, metal is forced to flow through a die aperture to

give a continuous prismatic shape All three process can be hot (T>0.85Tm), warm

(0.55Tm<T<0.85Tm) or cold (T<0.35Tm) Inspinning, a spinning disk of ductile metal

(195)

tear or to fold back on itself (‘‘lapping’’) Hot forging of metals allows larger changes of shape but generally gives a poor surface and tolerance because of oxidation and warpage Cold forging gives greater precision and finish, but forging pressures are higher and the deformations are limited by work hardening

Powder methods (Figure 7.8) These methods create the shape by pressing and then sintering fine particles of the material The powder can be cold-pressed and then sintered (heated at up to 0.8Tmto give bonding); it can be pressed in a heated die (‘‘die-pressing’’); or, contained in a thin preform, it can be heated under a hydrostatic pressure (‘‘hot isostatic pressing’’ or ‘‘HIPing’’) Metals that are too high-melting to cast and too strong to deform, can be made (by chemical methods) into powders and then shaped in this way But the processes are not limited to ‘‘difficult’’ materials; almost any material can be shaped by subjecting it, as a powder, to pressure and heat

Powder processing is most widely used for small metallic parts like gears and bearings for cars and appliances It is economic in its use of material, it allows parts to be fabricated from materials that cannot be cast, deformed or machined, and it can give a product that requires little or no finishing Since pressure is not transmitted uniformly through a bed of powder, the length of a die-pressed powder part should not exceed 2.5 times its diameter Sections must be near-uniform because the powder will not flow easily around corners And the shape must be simple and easily extracted from the die

Ceramics, difficult to cast and impossible to deform, are routinely shaped by powder methods In slip casting, a water-based powder slurry is poured into a plaster mold The mold wall absorbs water, leaving a semi-dry skin of slurry over its inner wall The remaining liquid is drained out, and the dried slurry shell is fired to give a ceramic body In powder injection molding (the way spark-plug insulators are made) a ceramic powder in a polymer binder is molded in the conventional way; the molded part is fired, burning of the binder and sintering the powder

Composite fabrication methods (Figure 7.9) These make polymer–matrix composites reinforced with continuous or chopped fibers Large components are fabricated by filament winding or by laying-up pre-impregnated mats of carbon, glass or Kevlar fiber (‘‘pre-preg’’) to the required thickness, pressing and curing Parts of the process can be automated, but it remains a slow manufacturing route; and, if the component is a critical one, extensive ultrasonic testing may be necessary to confirm its integrity Higher integrity is given by vacuum- or pressure-bag molding, which squeezes bubbles out of the matrix before it polymerizes Lay-up methods are best suited to a small number of high-performance, tailor-made, components More routine components (car bumpers, tennis racquets) are made from chopped-fiber composites by pressing and heating a ‘‘dough’’ of resin containing the fibers, known as bulk molding compound (BMC) or sheet molding compound

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Powder Die

Furnace

Press

Sinter

Die-pressing and sintering

Thin preform

Powder Pressure

vessel

Pressure P, temperature T,

time t

Hot isostatic pressing

Heater Screw

Heating elements Debind

and sinter

Powder and binder Split, heated mold

Nozzle Cylinder

Powder injection molding

Porous mold

Casting Draining Sintering

Slip casting

Figure 7.8 Powder processing Indie-pressing and sinteringthe powder is compacted in a die, often with a binder, and the green compact is then fired to give a more or less dense product Inhot isostatic pressing, powder in a thin, shaped, shell or pre-form is heated and compressed by an external gas pressure Inpowder injection molding, powder and binder are forced into a die to give a green blank that is then fired Inslip casting, a

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(SMC), in a mold, or by injection molding a rather more fluid mixture into a die The flow pattern is critical in aligning the fibers, so that the designer must work closely with the manufacturer to exploit the composite proper-ties fully

Rotating mandrel

Fibers of glass, carbon

or Kevlar

Resin

Filament winding

Mold Lay-upreinforcement

Brush on resin Roll

Mold

Resin Fiber roving Resin

Chopped fiber

Roll and spray lay-up

Pump Resin + glass Release coat Mold

Pump

Flexible bag

Resin + glass

Release coat Mold

Flexible bag Heater

(b) Pressure bag (a) Vacuum bag

Heater

Vacuum- and pressure-bag molding Pultrusion

Drive rollers Heated die

Reinforcement

Resin Cutter

Composite sections

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Rapid prototyping systems (RPS — Figure 7.10) The RPS allow single examples of complex shapes to be made from numerical data generated by CAD solid-modeling software The motive may be that of visualization: the aesthetics of an object may be evident only when viewed as a prototype

Platform

Workpiece Laser beam

Mirror

Laser

Photosensitive resin Table

Thermoplastic filament

Workpiece Heated

head

Bonded sand

Print head Sand

spreader Sand

feed

Workpiece Paper supply

Table Heated roller Light beam

Mirror

Deposition modeling

Direct mold modeling Laminated object manufacture, LOM

Stereo-lithography, SLA

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It may be that of pattern-making: the prototype becomes the master from which molds for conventional processing, such as casting, can be made or — in complex assemblies — it may be that of validating intricate geometry, ensuring that parts fit, can be assembled, and are accessible All RPS can create shapes of great complexity with internal cavities, overhangs and transverse features, though the precision, at present, is limited to0.3 mm at best

All RP methods build shapes layer-by-layer, rather like three-dimensional (3D) printing, and are slow (typically 4–40 h per unit) There are at least six broad classes of RPS:

(i) The shape is built up from a thermoplastic fed to a single scanning head that extrudes it like a thin layer of toothpaste (‘‘fused deposition modelling’’ or FDM), exudes it as tiny droplets (‘‘ballistic particle manufacture’’, BPM), or ejects it in a patterned array like a bubble-jet printer (‘‘3D printing’’)

(ii) Scanned-laser induced polymerization of a photo-sensitive monomer (‘‘stereo-lithography’’ or SLA) After each scan, the work piece is incrementally lowered, allowing fresh monomer to cover the surface Selected laser sintering (SLS) uses similar laser-based technology to sinter polymeric powders to give a final product Systems that extend this to the sintering of metals are under development

(iii) Scanned laser cutting of bondable paper elements Each paper-thin layer is cut by a laser beam and heat bonded to the one below (iv) Screen-based technology like that used to produce microcircuits (‘‘solid

ground curing’’ or SGC) A succession of screens admits UV light to polymerize a photo-sensitive monomer, building shapes layer by layer (v) SLS allows components to be fabricated directly in thermoplastic, metal or ceramic A laser, as in SLA, scans a bed of particles, sintering a thin surface layer where the beam strikes A new layer of particles is swept across the surface and the laser-sintering step is repeated, building up a 3-dimensional body

(vi) Bonded sand molding offers the ability to make large complex metal parts easily Here a multi-jet print-head squirts a binder onto a bed of loose casting sand, building up the mold shape much as selected laser sintering does, but more quickly When complete the mold is lifted from the remaining loose sand and used in a conventional casting process To be useful, the prototypes made by RPS are used as masters for silicone molding, allowing a number of replicas to be cast using high-temperature resins or metals

Machining (Figure 7.11) Almost all engineering components, whether made of metal, polymer, or ceramic, are subjected to some kind of machining during manufacture To make this possible they should be designed to make gripping and jigging easy, and to keep the symmetry high: symmetric shapes need fewer

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operations Metals differ greatly in theirmachinability,a measure of the ease of chip formation, the ability to give a smooth surface, and the ability to give economical tool life (evaluated in a standard test) Poor machinability means higher cost

Cut

Turning

Milling

Workpiece Feed

Cut Tool

Tool

Workpiece

Turning and milling

Punch

Die Pressure

pad

Deep drawing Blanking

Bending Stretching

Blank

Drawing, blanking, bending and stretching

Abrasive reservoir Water

from pump

Mixing chamber Sapphire die

Abrasive water jet Water jet

Water-jet cutting

Graphite electrode Servo-controlled hydraulic feed

Dielectric fluid Workpiece Insulator +

-Electro-discharge machining

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